Both Uses of

muse
in
Anne Of Green Gables

In school I can look at her and muse over days departed.
p. 129.3

muse = reflect (remember and think about)

"You'd better muse over your lessons and sums," said Marilla, concealing her delight at this development of the situation.
p. 129.3 *

muse = reflect (think) deeply on a subject

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.