General:
* Ponder
* Mull over
* Ruminate
* Contemplate
* Weigh
* Deliberate
* Cogitate
* Meditate
* Reflect
* Muse
More Specific:
* Scrutinize (for examining details)
* Discern (for recognizing subtle differences)
* Dissect (for analyzing thoroughly)
* Probe (for investigating deeply)
* Evaluate (for assessing worth or quality)
* Analyze (for breaking down into components)
* Synthesize (for combining ideas)
* Assimilate (for absorbing information)
* Internalize (for making something a part of oneself)
Figurative:
* Brew (for ideas forming in the mind)
* Ferment (for ideas developing and changing)
* Chew over (for thinking deeply and repeatedly)
* Turn over in one's mind (for thinking about something persistently)
You can choose the verb that best suits the context and the level of thoughtfulness you want to convey. For example, "ponder" suggests a slow and deliberate consideration, while "scrutinize" implies a close and detailed examination.