All 5 Uses of

muse
in
The Count of Monte Cristo

Signor Pastrini remained silent a short time; it was evident that he was musing over this answer, which did not seem very clear.†
Chpt 33-34 *

musing = reflecting (thinking) -- perhaps aloud

The actors made their entries and exits unobserved or unthought of; at certain conventional moments, the spectators would suddenly cease their conversation, or rouse themselves from their musings, to listen to some brilliant effort of Moriani's, a well-executed recitative by Coselli, or to join in loud applause at the wonderful powers of La Specchia; but that momentary excitement over, they quickly relapsed into their former state of preoccupation or interesting conversation.†
Chpt 33-34

musings = thoughts

Well, then, it is to see a thing on which I have sometimes mused for hours together.†
Chpt 59-60

mused = thought -- possibly aloud

How often did he muse over it and pronounce the name of a dear friend—a friend lost to him forever; and on his death-bed, when the near approach of eternity seemed to have illumined his mind with supernatural light, this thought, which had until then been but a doubt, became a conviction, and his last words were, 'Maximilian, it was Edmond Dantes!'†
Chpt 49-50

Since then the maid had been below, and like every one else she thought the young ladies were in their own room; Madame Danglars, therefore, went to bed without a shadow of suspicion, and began to muse over the recent events.†
Chpt 99-100 *

Definitions:

(1) (muse as in: her musings)
reflect (think) deeply on a subject -- perhaps aloud
(2) (muse as in: She was his muse)
the source of an artist's inspiration - especially a person or mythological goddess

The 9 muses were the daughters of the Greek gods Zeus & Mnemosyne. Each of the muses was thought to inspire and preside over one of the arts.
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

More rarely, muse is used as a synonym for "poet". In Shakespeare's time, muse could be used in the sense of being astonished or puzzled by something strange or unexpected.