muse

To muse is to think about something in a leisurely, contemplative way: She mused on what might have been.

The word suggests reflective pondering rather than urgent problem-solving.

As a noun, a muse is a source of inspiration, especially for artists and writers—someone or something that sparks creative work: His wife was his muse for thirty years. (Capitalized Muse refers to the Greek goddesses of the arts.)