Belief in belief: My solution to the final exam. Harry, being familiar with logic problems would plausibly try to violate the parseltongue curse using Godel's methods. He does not know that this would not work, and would not be able to test it in his current situation without being shot. Harry could in this situation reasonably conclude that knowing the exact mechanics of the parseltongue curse is critically important, and knowing the prophecy speaks of him ending the world and that he and Voldemort are literal kindred spirits, it is possible that sharing secrets with Voldemort might cause the end of the world. It is also possible that not sharing secrets with Voldemort might end the world. Since there are too many unknowns for Harry to make a choice one way or the other the path of least risk is to ask for more information.In order to verify the information Voldemort needs to explain to him how parseltongue works and allow Harry to test Voldemorts explanation. Therefore Harry's first move should be to say: "Yesss, have power you know not. If not sshared world may end." (This is plausibly true of partial transfiguration.) The only reasonable move for Voldemort to make is to demand Harry tell him. At which point Harry may truthfully reply: "If sshared, chansse world may end. Do not know which risssk greater and cannot determine without certain information you have."