Provide inspiration for puzzle (6)

I believe the answer is:

bemuse

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

'for puzzle' is the definition.
(I've seen this in another clue)

'provide inspiration' is the wordplay.
'provide' becomes 'be' (I can't justify this - if you can you should give a lot more credence to this answer).
'inspiration' becomes 'muse' (a muse is someone's inspiration).
'be'+'muse'='BEMUSE'

Can you help me to learn more?

(Other definitions for bemuse that I've seen before include "Stupefy, puzzle" , "Confound" , "Fox" , "Confuse, bewilder" , "Puzzle and confuse" .)

I've seen this clue in The Sun, The Telegraph, The Globe and Mail, The Guardian and The Times.

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