What should we do when we disagree?

You and I have been colleagues for ten years, during which we have tirelessly discussed the reasons both for and against the existence of God. There is no argument or piece of evidence bearing directly on this question that one of us is aware of that the other is not—we are, then, evidential equals relative to the topic of God’s existence. There is also no cognitive virtue or capacity, or cognitive vice or incapacity, that one of us possesses that the other does not—we are, then, also cognitive equals relative to the question at issue. Given this evidential and cognitive equality, combined with the fact that we have fully disclosed to one another all of our reasons and arguments relative to this topic, we are epistemic peers with respect to the question whether God exists. Yet despite the symmetry of our epistemic positions, we deeply disagree about the answer to this question. What response does rationality require in such a case, where epistemic peers disagree over a question despite there being no apparent asymmetries between them?