How can a perfect, unchanging god do anything?

You often hear theists, particularly Christians, claim that their god is perfect and unchanging. But for this god to accomplish anything, he has to change from inaction to action with regards to that objective. For example, to answer a prayer, such a god would have to change from not acting on it to fulfilling it. Isn't this a logical contradiction? How do theists who believe their god is unchanging square this circle?