reflect (think) deeply on a subject -- perhaps aloud
"Why, Trumbull himself is pretty sure of five hundred—_that_ you may depend,—I shouldn’t wonder if my brother promised him," said Solomon, musing aloud with his sisters, the evening before the funeral.
…Lydgate thought that after all his wild mistakes and absurd credulity, he had found perfect womanhood—felt as if already breathed upon by exquisite wedded affection such as would be bestowed by an accomplished creature who venerated his high musings and momentous labors and would never interfere with them; who would create order in the home and accounts with still magic, yet keep her fingers ready to touch the lute and transform life into romance at any moment; who was instructed to…
There are no more uses of "muse" identified with this meaning, but check unspecified meaning below.
Show samples from other sources
He mused aloud about the afternoon’s developments.
Let me muse on it on a while and I’ll get back to you.