Muse

–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; Middle English musen to mutter, gaze meditatively on, be astonished < Middle French muser, perhaps ultimately derivative of Medieval Latin mūsum muzzle

—Related forms
mus·er, noun

—Can be confused:   mews, muse .

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

(dictionary.com)