Think quietly about me touring the States (4)

I believe the answer is:

muse

I'm a little stuck... Click here to teach me more about this clue!

'think quietly' is the definition.
'muse' can be an answer for 'think' (to muse on something is to think about it). I am unsure of the 'quietly' bit.

'me touring the states' is the wordplay.
'touring' is an insertion indicator (tour can mean to go around).
'the states' becomes 'US' (abbreviation for the United States).
'me' enclosing 'us' is 'MUSE'.

'about' is the link.

Can you help me to learn more?

(Other definitions for muse that I've seen before include "Ponder in meditative way" , "Ponder or meditate" , "Contemplation" , "Cogitate" , "Goddess; rock group" .)

I've seen this clue in the Evening Standard.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.