What news does the Oedipus promise priest in play

In the play "Oedipus Rex" by Sophocles, Oedipus promises the priest to do whatever he can to help find the murderer of Laius, the former king of Thebes. Oedipus swears to do everything in his power to find the truth and punish the guilty, regardless of who they may be, even if it means uncovering the most terrible secrets.