Use 'cogitate' to imply a profound level of thinking, more than just a quick consideration. The philosopher loves to cogitate on existential questions.
Pro Tip 2/3
Time-Intensive
'Cogitate' suggests spending a significant amount of time in thought. She's cogitating on her future career path.
Pro Tip 3/3
Serious Subjects
Typically used for serious, complex, or important topics, not trivial ones. The committee will need to cogitate on this proposal.