What action has Oedipus taken to find an answer to the city's problems?

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Oedipus, as a good Greek, knows that things like pestilence are a sign that not all is well with the gods. The priest comes to Oedipus and confirms this point. Oedipus knows that he must seek counsel. The place to go is clear - the Oracle of Delphi. So, he sends his brother-in-law, Creon.

When Creon returns, Creon asks if Oedipus wants to hear the counsel of Apollo in private. Oedipus wants him just to speak. Creon does. Crean reveals that Laius, the former ruler of Thebes was murdered. The oracle also gives a directive. The murder, who still dwells in Thebes, must be driven out. Oedipus is shocked by this revelation. 

Oedipus, therefore, knows what he needs to do: find the murderer and drive him out. Therefore, he is passionate about finding the murderer to save Thebes. 

When the problem proves to be intractable, Oedipus sends for the blind prophet, Tiresias.  Tiresias is cryptic in his speech, as he knows the truth. When Oedipus persists in pressing the prophet, Tiresias finally divulges the truth. In the end, Oedipus assumes responsibility and the play ends. Oedipus is truly a tragic hero.