One cut out to make an entry, perhaps (6)

I believe the answer is:

coupon

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'one cut' is the definition.
The definition and answer can be both related to thinking as well as being singular nouns.
Maybe there's an association between them I don't understand?

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for coupon that I've seen before include "Entry form" , "means to buy goods" , "Voucher or ticket" , "Token" , "betting slip" .)

I've seen this clue in the Evening Standard.

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