excogitate
verb
°To think over something carefully; to consider fully; cogitate.
"2007: Did he ponder the harmony of the spheres? Certainly not: celestial spheres were first excogitated decades or more after Pythagoras' death. — MF Burnyeat, ‘Other Lives’, London Review of Books 29:4, p. 3"
°To come to a conclusion through reason or careful thought.
"After many years of study, he excogitated a solution."