Although Socrates influenced Plato directly as related in the dialogues, the influence of Pythagoras upon Plato also appears to have significant discussion in the philosophical literature. Pythagoras, or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of Plato. According to R. M. Hare, this influence consists of three points: (1) The platonic Republic might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton. (2) There is evidence that Plato possibly took from Pythagoras the idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for substantial theses in science and morals". (3) Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world". It is probable that both were influenced by Orphism. Pythagoras held that all things are number, and the cosmos comes from numerical principles. The physical world of becoming is an imitation of the mathematical world of being. This ideas were very influential in Heraclitus, Parmenides and Plato. Aristotle claimed that the philosophy of Plato closely followed the teachings of the Pythagoreans, and Cicero repeats this claim: "They say Plato learned all things Pythagorean" (Platonem ferunt didicisse Pythagorea omnia). George Karamanolis notes that Numenius accepted both Pythagoras and Plato as the two authorities one should follow in philosophy, but he regarded Plato's authority as subordinate to that of Pythagoras, whom he considered to be the source of all true philosophy--including Plato's own. For Numenius it is just that Plato wrote so many philosophical works, whereas Pythagoras' views were originally passed on only orally. The precise relationship between Plato and Socrates remains an area of contention among scholars. Plato makes it clear in his Apology of Socrates that he was a devoted young follower of Socrates. In that dialogue, Socrates is presented as mentioning Plato by name as one of those youths close enough to him to have been corrupted, if he were in fact guilty of corrupting the youth, and questioning why their fathers and brothers did not step forward to testify against him if he was indeed guilty of such a crime (33d-34a). Later, Plato is mentioned along with Crito, Critobolus, and Apollodorus as offering to pay a fine of 30 minas on Socrates' behalf, in lieu of the death penalty proposed by Meletus (38b). In the Phaedo, the title character lists those who were in attendance at the prison on Socrates' last day, explaining Plato's absence by saying, "Plato was ill". (Phaedo 59b) Plato never speaks in his own voice in his dialogues. In the Second Letter, it says, "no writing of Plato exists or ever will exist, but those now said to be his are those of a Socrates become beautiful and new" (341c); if the Letter is Plato's, the final qualification seems to call into question the dialogues' historical fidelity. In any case, Xenophon and Aristophanes seem to present a somewhat different portrait of Socrates from the one Plato paints. Some have called attention to the problem of taking Plato's Socrates to be his mouthpiece, given Socrates' reputation for irony and the dramatic nature of the dialogue form. Aristotle attributes a different doctrine with respect to Forms to Plato and Socrates (Metaphysics 987b1-11). Aristotle suggests that Socrates' idea of forms can be discovered through investigation of the natural world, unlike Plato's Forms that exist beyond and outside the ordinary range of human understanding. Mythos and logos are terms that evolved along classical Greece history. In the times of Homer and Hesiod (8th century BC) they were quite synonyms, and contained the meaning of tale or history. Later came historians like Herodotus and Thucydides, as well as philosophers as Parmenides and other Presocratics that introduced a distinction between both terms, and mythos became more a nonverifiable account, and logos a rational account. Plato, being a disciple of Socrates, and a strong partisan of philosophy based on logos, it seems that should have avoided the use of myth-telling. Instead he made an abundant use of it. This fact has produced analytical and interpretative work, in order to clarify the reasons and purposes for that use. Plato, in general, distinguished between three types of myth. First there were the false myths, like those based on stories of gods subject to passions and sufferings, because reason teaches that God is perfect. Then came the myths based on true reasoning, and therefore also true. Finally there were those non verifiable because beyond of human reason, but containing some truth in them. Regarding the subjects of Plato's myths they are of two types, those dealing with the origin of the universe, and those about morals and the origin and fate of the soul. It is generally agreed that the main purpose for Plato in using myths was didactic. He considered that only a few people were capable or interested in following a reasoned philosophical discourse, but men in general are attracted by stories and tales. Consequently then, he used the myth to convey the conclusions of the philosophical reasoning. Some of Plato's myths were based in traditional ones, others were modifications of them, and finally he also invented altogether new myths.

Answer this question "Was there any specific type of a myth that Plato mentions?" by extracting the answer from the text above.
Plato, in general, distinguished between three types of myth.