speculate vs muse

speculate is not a noun while muse is a noun.

Word	Noun	Adjective	Verb	Adverb
speculate	No	No	Yes	No
muse	Yes	No	Yes	No

As verbs, speculate and muse are synonyms defined as:

Other synonyms of speculate include chew over, contemplate, excogitate, meditate, mull, mull over, ponder, reflect, ruminate, think over.

speculate (noun)	muse (noun)
	the source of an artist's inspiration

speculate (verb)	muse (verb)
reflect deeply on a subject	reflect deeply on a subject
to believe especially on uncertain or tentative grounds
talk over conjecturally, or review in an idle or casual way and with an element of doubt or without sufficient reason to reach a conclusion
invest at a risk