ideate: (id8)

analyze, appraise, brood,
comprehend, consider, deliberate,
evaluate, examine, figure out,
have in mind, imagine, intellectualize,
judge, mull over, muse, ponder,
put on one's thinking cap,
rack one's brains, rationalize, reason,
reflect, resolve, ruminate, sort out,
speculate, stew, stop to consider,
study, take under consideration,
turn over, use one's head, weigh.