All 8 Uses

muse
in
A Tale of Two Cities
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"That's a coincidence, too," the guard mused, "for I made the same of it myself."†
Chpt 1.2 *
He watched her as she mused, and the moment she raised her eyes again, went on: "In your adopted country, I presume, I cannot do better than address you as a young English lady, Miss Manette?"†
Chpt 1.4
Depressed and slinking though they were, eyes of fire were not wanting among them; nor compressed lips, white with what they suppressed; nor foreheads knitted into the likeness of the gallows-rope they mused about enduring, or inflicting.†
Chpt 1.5
Time was, when a poet sat upon a stool in a public place, and mused in the sight of men.†
Chpt 2.14
Mr. Cruncher, sitting on a stool in a public place, but not being a poet, mused as little as possible, and looked about him.†
Chpt 2.14
Games at cards languished, players at dominoes musingly built towers with them, drinkers drew figures on the tables with spilt drops of wine, Madame Defarge herself picked out the pattern on her sleeve with her toothpick, and saw and heard something inaudible and invisible a long way off.†
Chpt 2.15
"French, eh?" repeated Carton, musing, and not appearing to notice him at all, though he echoed his word.†
Chpt 3.8
"At Tellson's banking-house at nine," he said, with a musing face.†
Chpt 3.12

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)
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.