From Longman Dictionary of Contemporary Englishreason something ↔ out phrasal verbTHINK ABOUTto find an explanation or solution to a problem, by thinking of all the possibilities SYN work out → reason→ See Verb table
Examples from the Corpus
reason out• All the way down to the rec room, she reasoned it out.• The fact substantiates what reason points out.• A. Then there's all the more reason to make out a covenant. let's say you pay tax at 40%.• Serious depression was the main reason I sought out a psychiatrist.• He has a second reason, spelled out in one of several stagy subplots.• For these reasons, and for the reasons set out in the judgment of Balcombe L.J., I would allow this appeal.• The reason he slipped out was to phone and make a few arrangements for them.• For the cat to reason this out would require considerable mental agility, but there is of course a simpler explanation. 