muse ~verb~ mused, mus·ing.

–verb (used without object)
1. to think or meditate in silence, as on some subject.
2. Archaic. to gaze meditatively or wonderingly.

–verb (used with object)
3. to meditate on.
4. to comment thoughtfully or ruminate upon.

Origin:
1300–50; ME musen to mutter, gaze meditatively on, be astonished <>

Synonyms:
1. cogitate, ruminate, think; dream. 1, 3. ponder, contemplate, deliberate.