excogitate
verb·/ɛkˈskɑː.dʒɪ.teɪt/
Think out with care, devise by deliberate mental effort. Ideas produced not by spark but by sustained turning-over. Work done in the mind's workshop, gears engaged.
She excogitated a solution on the train, staring out at winter fields as if they were diagrams.
Etymology
From Latin excogitāre “to think out,” from ex- “out” + cogitāre “to think.” The prefix matters: thought drawn forth, extracted from the raw.
Related Words
cogitateto think; less emphatically “worked out”
deviseto plan or invent; more common
ruminateto turn over in the mind; slower, sometimes circular
contriveto devise, often with a hint of artifice