reason (something) out
To come to a logical conclusion for, determination about, or solution to something. Well, let's just reason the problem out—there has to be a way to fix this without costing us a fortune. You're wasting your time trying to reason his motivations out. Dan just does things according to his own odd beliefs.
reason something out
to figure something out; to plan a reasonable course of action. Now let's be calm and try to reason this out. Let us reason out our difficulties.
reason out
v. To determine or conclude something by logical thinking: The detective reasoned out the killer's motive. The mechanics were able to reason out the problem from the little I told them. Rather than worrying about the decision, let's sit down and reason it out.