DESCRIPTION CYCLIC POLY (PHENYLENE ETHER ETHER KETONE) COMPOSITION AND METHOD FOR PRODUCING THE SAME TECHNICAL FIELD [0001] The present invention relates to a composition comprising a cyclic poly(phenylene ether ether ketone) and a production method thereof. More particularly, the present invention relates to a cyclic poly (phenylene ether ether ketone) composition comprising not less than 60% by weight of a cyclic poly (phenylene ether ether ketone), which is characterized by having a low melting point and excellent processability at a low temperature. BACKGROUND ART [0002] Recently, aromatic cyclic compounds are drawing attention its application/development potential as a high-performance material or functional material based on the properties arising from the cyclic structure (e.g., as a compound having clathrating capacity and as a effective monomer in the synthesis of a high-molecular-weight linear polymer by ring-opening polymerization) as well as for its structure-derived specificity. Cyclic poly (phenylene ether ether ketone)s are also noteworthy in the same manner since they belong to the category of aromatic cyclic compounds. [0003] As a method of synthesizing a cyclic poly (phenylene ether ether ketone), there is reported, for example, a method in which a linear poly (phenylene ether ether ketone) oligomer having a hydroxyl group at both terminals and a linear poly (phenylene ether ether ketone) oligomer having a fluorine group at both terminals are reacted as shown in the following reaction formula (for example, see Non-patent Document 1). [0004] [Formula 1] [0005] In this method, since long-chain oligomers are used as starting materials, the resulting poly (phenylene ether ether ketone) mixture is composed of cyclic poly (phenylene ether ether ketone) having a repeating number (m) of 3 and/or 6; therefore, this method can yield only a cyclic poly (phenylene ether ether ketone) having a melting point higher than 270°C. More specifically, it is described that the cyclic poly (phenylene ether ether ketone)s obtained from these linear oligomers shown in the above reaction formula (an oligomer having a hydroxyl group at both terminals, which is constituted by 4 benzene ring component units; and an oligomer having a fluorine group at both terminals, which is constituted by 5 benzene ring component units) are composed of only a cyclic trimer (m = 3) and cyclic hexamer (m = 6), which are cyclic poly (phenylene ether ether ketone)s having a melting point of 366°C and 324°C, respectively. Further, Non-patent Document 1 also offers descriptions regarding the synthesis of a poly (phenylene ether ether ketone) by ring-opening polymerization of a cyclic poly (phenylene ether ether ketone); however, the cyclic poly (phenylene ether ether ketone) used therein is the one having a high melting point obtained in the above-described method. Moreover, the ring-opening polymerization is performed only in a temperature range of not lower than 340°C, that is, a temperature range which is not lower than the melting point of the poly (phenylene ether ether ketone), and there is no description at all with regard to ring- . opening polymerization at a temperature not lower than the melting point of the poly (phenylene ether ether ketone). [0006] Further, the same authors also discloses a method of producing a cyclic poly (phenylene ether ether ketone) by reacting a linear poly (phenylene ether ether ketone) oligomer having a hydroxyl group at both terminals with 4,4'-difluorobenzophenone as shown in the following reaction formula (for example, see Non-patent Document 2). [0007] [Formula 2] HO-0-O-OK>O-OOH * t-O-t-O* [0008] It is described that the cyclic poly (phenylene ether ether ketone) obtained by this method is a mononuclear compound of a cyclic dimer (m = 2) and has a melting point of not lower than 440°C. In this manner, the use of a linear poly (phenylene ether ether ketone) oligomer as a material for synthesizing a cyclic poly (phenylene ether ether ketone) can be considered as a significant method for the purpose of obtaining a cyclic poly (phenylene ether ether ketone) having a desired repeating number (m) in a high purity; however, by this method, it is difficult to produce the cyclic poly (phenylene ether ether ketone) composition of the present invention, which is characterized by being a mixture composed of cyclic poly (phenylene ether ether ketone)s having different repeating numbers (m) and having a melting point of not higher than 270°C. Further, in the synthesis of a cyclic poly (phenylene ether ether ketone) according to Non-patent Documents 1 and 2, since the reaction is performed under pseudo-high-dilution conditions, although the selectivity for the generation of cyclic poly (phenylene ether ether ketone) is high, an ultra-dilute condition must be maintained, so that the reaction requires an extremely long time. In addition, it is also required to perform the step of separately preparing the oligomer having a hydroxyl group at both terminals and the oligomer having a fluorine group at both terminals that are used as the materials for the synthesis of cyclic poly (phenylene ether ether ketone). Therefore, it is difficult to say that the methods according to Non-patent Documents 1 and 2 are industrially applicable production methods of a cyclic poly (phenylene ether ether ketone). [0009] Further, there is also reported a method using an aromatic imine compound as a starting material for producing a cyclic poly (phenylene ether ether ketone) (for example, see Non-patent Document 3). Non-patent Document 3 discloses a method in which a cyclic poly (phenylene ether ether ketimine) is prepared from N-phenyl (4,4'-difluorodiphenyl) ketimine and hydroquinone as shown in the following reaction formula and the resulting cyclic poly (phenylene ether ether ketimine) is then hydrolyzed in an acidic condition to obtain a cyclic poly (phenylene ether ether ketone). [0010] [Formula 3] [0011] Since an aromatic ketimine compound generally has a low reactivity as compared to the corresponding aromatic ketone compound and the reaction is performed in an ultra-dilute condition, even after the completion of the synthesis reaction of the cyclic poly (phenylene ether ether ketimine), a low-molecular-weight linear oligomer, which is difficult to be separated from the cyclic poly (phenylene ether ether ketimine), remains. Therefore, this method can yield only a low-purity cyclic poly (phenylene ether ether ketone) containing a large amount of impurities. In addition, in order to produce a cyclic poly (phenylene ether ether ketone) by this method, it is indispensable to perform multiple complicated reaction steps, including at least the steps of preparing an aromatic ketimine compound used as a starting material; preparing and purifying a cyclic poly (phenylene ether ether ketimine); and preparing and purifying a cyclic poly (phenylene ether ether ketone) by hydrolyzing the thus obtained cyclic poly (phenylene ether ether ketimine). Therefore, it is difficult to say that this method is an industrially applicable production method of a cyclic poly (phenylene ether ether ketone). Furthermore, although there is no description in Non-patent Document 3 with regard to the melting point of the resulting cyclic poly (phenylene ether ether ketone), since it contains a large amount of linear poly (phenylene ether ether ketone) having a high melting point as an impurity, it is believed that the cyclic poly (phenylene ether ether ketone) obtained by this method has, unlike the one according to the present invention, a high melting point. Moreover, Non-patent Document 3 offers no description at all with regard to ring-opening polymerization of the cyclic poly (phenylene ether ether ketone) obtained by this method. [0012] Further, there is also disclosed a method of producing a cyclic poly (phenylene ether ether ketone) using a phenylene ether oligomer as a starting material (for example, see Patent Document 1). [0013] [Formula 4] [0014] In Patent Document 1, it is described that a cyclic poly (phenylene ether ether ketone) can be prepared in a single step by a reaction of 1,4-diphenoxybenzene in the presence of a Lewis acid. Synthesis methods of poly (phenylene ether ketone)-type compounds can be generally classified into two types: synthesis methods based on ether bond formation by aromatic nucleophilic substitution reaction and synthesis methods based on ketone bond formation by aromatic electrophilic substitution reaction, and the route of the cyclic poly (phenylene ether ether ketone) synthesis according to Patent Document 1 is included in the latter type. One of the problems of using an aromatic electrophilic substitution reaction for the synthesis of a poly (phenylene ether ether ketone) is that the regioselectivity of the reaction is low. Therefore, the cyclic poly (phenylene ether ether ketone) obtained by the method described in Patent Document 1, too, is speculated to have a low purity, containing ortho-form and meta-form in addition to the desired para-form. Moreover, Patent Document 1 offers no description at all with regard to the melting point of the resulting cyclic poly (phenylene ether ether ketone). PRIOR ART DOCUMENTS PATENT DOCUMENTS [0015] Patent Document 1: CN 101519399 A NON-PATENT DOCUMENTS [0016] Non-patent Document 1: Macromolecules 1996,29, 5502 Non-patent Document 2: Macromol. Chem. Phys. 1996,197,4069 Non-patent Document 3: Polymer Bulletin 1999,42,245 SUMMARY OF THE INVENTION PROBLEMS TO BE SOLVED BY THE INVENTION [0017] An object of the present invention is to provide a novel cyclic poly (phenylene ether ether ketone) composition in which the problems of those cyclic poly (phenylene ether ether ketone)s obtained by the above-described prior arts, that is, high melting point and poor processability, are solved. More particularly, an object of the present invention is to provide a cyclic poly (phenylene ether ether ketone) composition comprising a cyclic poly (phenylene ether ether ketone), which has a superior property, that is, a low melting point, and can be synthesized by a simple method. MEANS FOR SOLVING THE PROBLEMS [0018] In order to solve the above-described problems, the following means are adopted in the present invention. That is, the present invention is as follows. 1. A cyclic poly (phenylene ether ether ketone) composition, which comprises not less than 60% by weight of a cyclic poly (phenylene ether ether ketone) represented by the following Formula (I), the cyclic poly (phenylene ether ether ketone) being a mixture of cyclic poly (phenylene ether ether ketone)s having different repeating numbers (m) and the composition having a melting point of not higher than 270°C: [0019] [Formula 5] [0020] (wherein, m represents an integer of 2 to 40). 2. The cyclic poly (phenylene ether ether ketone) composition according to 1, which is characterized in that the cyclic poly (phenylene ether ether ketone) is a mixture composed of cyclic poly (phenylene ether ether ketone)s having at least 3 different integers (m). 3. The cyclic poly (phenylene ether ether ketone) composition according to 1 or 2, which is characterized in that the cyclic poly (phenylene ether ether ketone) is a mixture composed of cyclic poly (phenylene ether ether ketone)s having at least 3 consecutive different integers (m). 4. The cyclic poly (phenylene ether ether ketone) composition according to any one of 1 to 3, which is characterized by having a reduced viscosity of not higher than 0.1 dL/g, the reduced viscosity being measured in sulfuric acid at 25°C. 5. A method of producing a poly (phenylene ether ether ketone), which is characterized in that the cyclic poly (phenylene ether ether ketone) composition according to any one of 1 to 4 is subjected to thermal ring-opening polymerization. 6. The method of producing a poly (phenylene ether ether ketone) according to 5, which is characterized in that the thermal ring-opening polymerization is performed at a temperature not higher than the melting point of the resulting poly (phenylene ether ether ketone). 7. The method of producing a poly (phenylene ether ether ketone) according to 5 or 6, which is characterized in that the thermal ring-opening polymerization is performed in the presence or absence of a catalyst 8. The method of producing a poly (phenylene ether ether ketone) according to 7, which is characterized in that the catalyst is an anionic polymerization initiator. 9. A method of producing the cyclic poly (phenylene ether ether ketone) composition according to any one of 1 to 4, which is characterized in that, when a mixture (Ml) comprising at least a dihalogenated aromatic ketone compound, dihydroxy aromatic compound, base (A) and organic polar solvent is allowed to react by heating to produce the cyclic poly (phenylene ether ether ketone) composition, the organic polar solvent is used in an amount of not less than 1.20 L with respect to 1.0 mol of benzene ring component in the mixture (Ml). 10. A method of producing the cyclic poly (phenylene ether ether ketone) composition according to any one of 1 to 4, which is characterized in that, when a mixture (M2) comprising at least a linear poly (phenylene ether ether ketone) represented by the following Formula (II), dihalogenated aromatic ketone compound, dihydroxy aromatic compound, base (A) and organic polar solvent is allowed to react by heating to produce the cyclic poly (phenylene ether ether ketone) composition, the organic polar solvent is used in an amount of not less man 1.20 L with respect to 1.0 mol of benzene ring component in the mixture (M2): [0021] [Formula 6] [0022] 11. The method of producing the cyclic poly (phenylene ether ether ketone) composition according to 9 or 10, which is characterized in that the dihydroxy aromatic compound is hydroquinone. 12. A method of producing the cyclic poly (phenylene ether ether ketone) composition according to any one of 1 to 4, which is characterized in that a mixture (M3) comprising at least a linear poly (phenylene ether ether ketone) represented by the following Formula (II), basic compound (B) and an organic polar solvent is allowed to react by heating [0023] [Formula 7] [0024] 13. The method of producing the cyclic poly (phenylene ether ether ketone) composition according to 12, which is characterized in that the mixture (M3) further contains water. 14. The method of producing the cyclic poly (phenylene ether ether ketone) composition according to 12 or 13, which is characterized in that the basic compound (B) contained in the mixture (M3) is an alkali metal halide. 15. The method of producing the cyclic poly (phenylene ether ether ketone) composition according to 12 or 13, which is characterized in that the basic compound (B) contained in the mixture (M3) is an alkali metal carbonate and/or alkali metal bicarbonate. EFFECTS OF THE INVENTION [0025] According to the present invention, a novel cyclic poly (phenylene ether ether ketone) composition comprising not less than 60% by weight of a cyclic poly (phenylene ether ether ketone), which is characterized by having a low melting point, can be provided. By this, the problems of those cyclic poly (phenylene ether ether ketone)s obtained by prior arts, that is, high melting point and poor processability, can be solved. MODE FOR CARRYING OUT THE INVENTION [0026] The present invention will now be described in more detail. [0027] (1) Cyclic poly (phenylene ether ether ketone) The cyclic poly (phenylene ether ether ketone) according to the present invention is a cyclic compound represented by the following Formula (I), which has p-phenylene ketone and p-phenylene ether as repeating structural unit. [0028] [Formula 8] [0029] In the Formula (I), the repeating number (m) is, for example, in the range of 2 to 40, preferably 2 to 20, more preferably 2 to 15, particularly preferably 2 to 10. The melting point of the cyclic poly (phenylene ether ether ketone) tends to be high when the repeating number (m) is large; therefore, from the standpoint of melting the cyclic poly (phenylene ether ether ketone) at a low temperature, it is preferred that the repeating number (m) be set in the above-described range. [0030] Further, the cyclic poly (phenylene ether ether ketone) represented by the Formula (I) is preferably a mixture composed of cyclic poly (phenylene ether ether ketone)s having different repeating numbers (m), more preferably at least 3 different repeating numbers (m), still more preferably at least 4 different repeating numbers (m), particularly preferably at least 5 different repeating numbers (m). Further, it is particularly preferred that these repeating numbers (m) be consecutive. As compared to a single compound having a single repeating number (m), a mixture composed of cyclic poly (phenylene ether ether ketone)s having different repeating numbers (m) tends to have a lower melting point. Also, as compared to a cyclic poly (phenylene ether ether ketone) mixture composed of cyclic poly (phenylene ether ether ketone)s having 2 different repeating numbers (m), the melting point of a mixture composed of cyclic poly (phenylene ether ether ketone)s having 3 or more different repeating numbers (m) tends to be even lower. Moreover, as compared to a mixture composed of cyclic poly (phenylene ether ether ketone)s having non-consecutive repeating numbers (m), a mixture composed of cyclic poly (phenylene ether ether ketone)s having consecutive repeating numbers (m) tends to have a further lower melting point. Here, the components of such cyclic poly (phenylene ether ether ketone)s having different repeating numbers (m) can be separated and analyzed by high-performance liquid chromatography. In addition, the composition of such cyclic poly (phenylene ether ether ketone)s, that is, the weight ratio of each cyclic poly (phenylene ether ether ketone) having the respective repeating number (m), can be calculated from the peak area ratio thereof obtained by high-performance liquid chromatography. [0031] Further, the cyclic poly (phenylene ether ether ketone) composition according to the present invention is characterized by having a melting point of not higher than 270°C, which is considerably lower than that of the corresponding linear poly (phenylene ether ether ketone). The melting point of the cyclic poly (phenylene ether ether ketone) composition is, for example, preferably not higher than 250°C, more preferably not higher than 230°C. The lower the melting point of the cyclic poly (phenylene ether ether ketone) composition, the lower the processing temperature thereof can be and the lower the processing temperature can be set when producing a polymer having a high polymerization degree using the cyclic poly (phenylene ether ether ketone) as a poly (phenylene ether ether ketone) prepolymer; therefore, a lower melting point is advantageous from the viewpoint that the energy required for processing can be reduced. Here, the melting point of the cyclic poly (phenylene ether ether ketone) composition can be determined by measuring the endothermic peak temperature using a differential scanning calorimeter. [0032] Further, the cyclic poly (phenylene ether ether ketone) composition according to the present invention comprises a cyclic poly (phenylene ether ether ketone) in an amount of not less than 60% by weight, preferably not less than 65%, more preferably not less than 70% by weight, still more preferably not less than 75% by weight. Examples of impurity component in the cyclic poly (phenylene ether ether ketone) composition, that is, a component other than the cyclic poly (phenylene ether ether ketone), mainly include linear poly (phenylene ether ether ketone)s. A linear poly (phenylene ether ether ketone) has a high melting point; therefore, when the weight ratio thereof is high, the melting point of the cyclic poly (phenylene ether ether ketone) composition tends to be high. Therefore, also from the viewpoints that the melting point of the cyclic poly (phenylene ether ether ketone) composition tends to be made low and that a poly (phenylene ether ether ketone) having a sufficiently high polymerization degree can be obtained when the cyclic poly (phenylene ether ether ketone) composition is used as a poly (phenylene ether ether ketone) prepolymer, it is preferred that the weight ratio of the cyclic poly (phenylene ether ether ketone) contained in the cyclic poly (phenylene ether ether ketone) composition be in the above-described range. [0033] The reduced viscosity (n) of the cyclic poly (phenylene ether ether ketone) composition according to the present invention which has the above-described characteristics is, for example, preferably not higher than 0.1 dL/g, more preferably not higher than 0.09 dL/g, still more preferably not higher than 0.08 dL/g. It is noted here that, in the present invention, the reduced viscosity refers to, unless otherwise specified, a value measured by an Ostwald viscosimeter at 25 °C for a concentrated sulfuric acid solution having a concentration of 0.1 g/dL (the weight of cyclic poly (phenylene ether ether ketone) composition or linear poly (phenylene ether ether ketone)/the volume of 98%-by-weight concentrated sulfuric acid) immediately after the dissolution in order to minimize the effect of sulfonation. Further, the reduced viscosity was calculated using the following equation: (wherein, t represents the transit time of the sample solution in seconds; tO represents the transit time of the solvent (98%-by-weight concentrated sulfuric acid); and C represents the concentration of the solution). [0034] Next, materials to be used in a preferred method of producing the cyclic poly (phenylene ether ether ketone) composition of the present invention will be described. [0035] (2) Dihalogenated aromatic ketone compound The dihalogenated aromatic ketone compound used in the present invention is an aromatic ketone compound represented by the following Formula (III): [0036] [Formula 9] [0037] In the Formula (III), X represents a halogeno group selected from fluorine, chlorine, bromine, iodine, astatine and the like, and the two halogeno groups may be the same or different. Specific examples of such dihalogenated aromatic ketone compound include 4,4'-difluorobenzophenone, 4,4'-dichlorobenzophenone, 4,4'-dibromobenzophenone, 4,4'-diiodobenzophenone, 4-fluoro-4'-chlorobenzophenone, 4-fluoro-4,-bromobenzophenone, 4-fluoro-4'-iodobenzophenone, 4-chloro-4'-bromobenzophenone, 4-chloro-4'-iodobenzophenone and 4-bromo-4'-iodobenzophenone. Among these, 4,4'-difluorobenzophenone is preferred from the standpoint of the reactivity and 4,4'-dichlorobenzophenone is preferred from the standpoint of the economic efficiency, and a particularly preferred specific example is 4,4'-difluorobenzophenone. These dihalogenated aromatic ketone compounds may be used individually, or two or more thereof may be used as a mixture. [0038] (3) Base (A) Examples of the base (A) used in the production of the cyclic poly (phenylene ether ether ketone) composition according to the present invention include alkali metal carbonates such as lithium carbonate, sodium carbonate, potassium carbonate, rubidium carbonate and cesium carbonate; alkaline earth metal carbonates such as calcium carbonate, strontium carbonate and barium carbonate; alkali metal bicarbonates such as lithium bicarbonate, sodium bicarbonate, potassium bicarbonate, rubidium bicarbonate and cesium bicarbonate; alkaline earth metal bicarbonates such as calcium bicarbonate, strontium bicarbonate and barium bicarbonate; alkali metal hydroxides such as lithium hydroxide, sodium hydroxide, potassium hydroxide, rubidium hydroxide and cesium hydroxide; and alkaline earth metal hydroxides such as calcium hydroxide, strontium hydroxide and barium hydroxide. Among these, from the standpoints of the ease of handling and reactivity, carbonates such as sodium carbonate and potassium carbonate and bicarbonates such as sodium bicarbonate and potassium bicarbonate are preferred. Sodium carbonate and potassium carbonate are more preferred and potassium carbonate is still more preferably used. These bases may be used individually, or two or more thereof may be used in combination without any problem. Further, these bases (A) are preferably used in the form of an anhydride; however, they may also be used in the form of a hydrate or as an aqueous mixture. It is noted here that the term "aqueous mixture" used herein refers to an aqueous solution, a mixture of an aqueous solution and a solid components), or a mixture of water and a solid component(s). [0039] (4) Dihydroxy aromatic compound The dihydroxy aromatic compound used in a preferred method of producing the cyclic poly (phenylene ether ether ketone) composition according to the present invention is an aromatic compound represented by the following Formula (TV): [0040] [Formula 10] [0041] In the Formula (TV), the repeating number (q) is not particularly restricted, and a preferred specific example of the dihydroxy aromatic compound is hydroquinone in which q is 0. Further, the upper limit of the repeating number (q) in the Formula (TV) is also not particularly restricted, and preferred examples of the dihydroxy aromatic compound include those in which q is 2 or smaller. These dihydroxy aromatic compounds may be used individually, or two or more thereof may be used as a mixture. [0042] The amount of the dihydroxy aromatic compound to be used is preferably in the range of 0.8 to 1.2 mol, more preferably 0.9 to 1.1 mol, still more preferably 0.95 to 1.05 mol, particularly preferably 0.98 to 1.03 mol. It is preferred that the dihydroxy aromatic compound be used in an amount in the above-described range since the decomposition reaction of the resulting cyclic poly (phenylene ether ether ketone) can be thereby inhibited and the generation of a linear poly (phenylene ether ether ketone), which is difficult to be separated from cyclic poly (phenylene ether ether ketone), tends to be suppressed. [0043] - (5) Organic polar solvent The organic polar solvent used in the method of producing the cyclic poly (phenylene ether ether ketone) composition according to the present invention is not particularly restricted as long as it does not substantially inhibit the reaction or cause undesirable side reactions such as decomposition of the resulting cyclic poly (phenylene ether ether ketone). Specific examples of such organic polar solvent include nitrogen-containing polar solvents such as N-methyl-2-pyrrolidone (NMP), N-methylcaprolactam, N,N-dimethylformamide (DMF), N,N-dimethylacetamide (DMAc), l,3-dimethyl-2-imidazolidinone (DMI), hexamethylphosphoramide and tetramethylurea; sulfoxide/sulfone-based solvents such as dimethyl sulfoxide (DMSO), dimethyl sulfone, diphenyl sulfone and sulfolane; nitrile-based solvents such as benzonitrile; diaryl ethers such as diphenyl ether; ketones such as benzophenone and acetophenone; and mixtures thereof. All of these organic polar solvents have high reaction stability and are, therefore, suitably used; however, preferred thereamong are N-methyl-2-pyrrolidone and dimethyl sulfoxide and N-methyl-2-pyrrolidone is particularly preferably used. These organic polar solvents are said to be preferable since they have excellent stability in a high temperature range, as well as from the standpoint of the availability. [0044] (6) Linear poly (phenylene ether ether ketone) The linear poly (phenylene ether ether ketone) in the present invention is a linear compound represented by the following Formula (II), which has p-phenylene ketone and p-phenylene ether as repeating structural unit. [0045] [Formula 11] [0046] In the Formula (II), the repeating number (n) is not particularly restricted; however, it is, for example, in the range of 10 to 10,000, preferably 20 to 5,000, more preferably 30 to 1,000. [0047] Further, the reduced viscosity (n) of the linear poly (phenylene ether ether ketone) in the present invention is not particularly restricted; however, in general, it is usually in the range of, for example, 0.1 to 2.5 dL/g, preferably 0.2 to 2.0 dL/g, more preferably 0.3 to 1.8 dL/g. Generally, the lower the reduced viscosity of a linear poly (phenylene ether ether ketone), that is, the lower the molecular weight of a linear poly (phenylene ether ether ketone), the higher the solubility thereof to an organic polar solvent becomes; therefore, a lower viscosity is advantageous in that the time required for the reaction can be reduced; however, any linear poly (phenylene ether ether ketone) can be used with no substantial problem as long as the reduced viscosity thereof is in the above-described range. [0048] The method of producing such linear poly (phenylene ether ether ketone) is not particularly restricted and any production method may be employed. For example, as represented by JP S54-90296A and JP S59-93724A, such linear poly (phenylene ether ether ketone) can be produced by performing a polycondensation reaction between an aromatic dihalogen compound and diphenol in the presence of an alkali salt. Moreover, molded articles, molding wastes, waste plastics, off-spec products and the like, in which a poly (phenylene ether ether ketone) produced by these methods are used, can be widely employed as well. [0049] Generally, production of a cyclic compound is based on competitive reactions of cyclic compound generation and linear compound generation; therefore, in a method for producing a cyclic poly (phenylene ether ether ketone), in addition to the desired cyclic poly (phenylene ether ether ketone), a linear poly (phenylene ether ether ketone) is generated as a by-product in no small amount. In the present invention, such by-product linear poly (phenylene ether ether ketone) can also be utilized without any problem; therefore, a method utilizing such linear poly (phenylene ether ether ketone), which is obtained by separating a cyclic poly (phenylene ether ether ketone) from a mixture containing the cyclic poly (phenylene ether ether ketone) and linear poly (phenylene ether ether ketone) generated by the later-described preferred production method of cyclic poly (phenylene ether ether ketone), is said to be a particularly preferred method. Conventionally, those linear compounds and linear poly (phenylene ether ether ketone)s that are generated as by¬product during the production of a cyclic compound or cyclic poly (phenylene ether ether ketone) have been considered to be of no utility value and thus disposed. Therefore, in the production of a cyclic compound, there are problems in that a large amount of waste is generated due to such by-product linear compounds and that the material monomer-based yield is low. In the present invention, such by-product linear poly (phenylene ether ether ketone)s can be utilized as a starting material, and this is of great significance from the standpoint of enabling a considerable decrease in the waste amount and a drastic improvement in the material monomer-based yield. [0050] Here, the form of the linear poly (phenylene ether ether ketone) is not particularly restricted, and it may be in the form of dry powder, granule, particle or pellet. It is also possible to use the linear poly (phenylene ether ether ketone) in a form containing an organic solvent, which is the reaction solvent, or in a form containing a third component which does not substantially inhibit the reaction. Examples of such third component include inorganic fillers and the linear poly (phenylene ether ether ketone) may also be used in the form of a resin composition containing an inorganic* filler. [0051] (7) Basic compound (B) As the basic compound (B) in the present invention, a wide range of known inorganic bases and organic bases can be used. Examples of the inorganic bases f include carbonates of alkali metals and .alkaline earth metals, such as lithium carbonate, sodium carbonate, potassium . carbonate, rubidium carbonate, cesium carbonate, calcium carbonate, strontium carbonate and barium carbonate; bicarbonates of alkali metals and alkaline earth metals, such as lithi um bicarbonate, sodium bicarbonate, potassium bicarbonate , rubidium bicarbonate, cesium bicarbonate, calcium bicarbonate, strontium bicarbonate and barium bicarbonate; hydroxides of alkali metals and alkaline earth metals, such as lithium hydroxide, sodium hydroxide, potassium hydroxide,, rubidium hydroxide, cesium hydroxide, calcium hydroxide, strontium hydroxide and barium hydroxide; phosphates of alkali metals and alkaline earth metals, such as X ithium phosphate, sodium phosphate, potassium phosphate, rubidium phosphatase , cesium phosphate, calcium phosphate, strontium phosphate and barium phosphate halides of alkali metals and alkaline earth metals, such as lithium fluoride, sodium fluoride, potassium fluoride, rubidium fluoride, cesium fluoride, calcium fluoride ^ strontium fluoride, barium fluoride, lithium chloride, sodium chloride, potassit_mjra chloride, rubidium chloride, cesium chloride, calcium chloride, strontium chlor-z£