reflect (think) deeply on a subject -- perhaps aloud
"So I am told, sir," returned Mr. George, still musing and looking on the ground.
He has more leisure for musing in Staple Inn and in the Rolls Yard during the long vacation than at other seasons, and he says to the two ’prentices, what a thing it is in such hot weather to think that you live in an island with the sea a-rolling and a-bowling right round you.
Is this Lady Dedlock standing beside the village beauty, smoothing her dark hair with that motherly touch, and watching her with eyes so full of musing interest?
"There never was," said my guardian, musing as he smiled upon me, "such a Dame Durden for making money last."
"I haven’t the least idea," said Richard, musing, "what I had better be.
There are no more uses of "muse" identified with this meaning, but check unspecified meaning below.
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He mused aloud about the afternoon’s developments.
Let me muse on it on a while and I’ll get back to you.