muse (the verb, not one of the daughters of Zeus) – to consider or meditate at at length
muse (the noun; again, not one of Zeus’ daughters) – a state of deep reflection
muse (still…not yet the offspring) – a guiding spirit; a source of inspiration; a poet
and
Muse (OK, now) – one of the nine daughters of Mnemosyne and Zeus, each of whom presided over a different art or science