The rational approach is to acknowledge that you do not have sufficient information to proceed, or acknowledge the various assumptions (better word than “belief) that you are using.
If you are using contradicting assumptions, then you should probably check to see if you are doing so because you want the conclusion that you are getting from the assumption.
We make decisions based on imperfect information and conflicting values every day. We generally can’t wait until we have sufficient information to proceed.
If you are using contradicting assumptions, then you should probably check to see if you are doing so because you want the conclusion that you are getting from the assumption.