Synonyms for Excogitate (same or very similar meaning)
WordNet sense 1 (come up with (an idea, plan, explanation, theory, or principle) after a mental effort):
contrive, devise, forge, formulate, inventWordNet sense 2 (reflect deeply on a subject):
contemplate, meditate, mull, muse, ponder, reflect, ruminate, speculate, chew over, mull over, think overFrom the ODE community, based on WordNetadd/edit