On the way out, concluded careful inspection (5-4)

I believe the answer is:

going-over

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'careful inspection' is the definition.
'going over' can be an answer for 'inspection' (going over is a kind of inspection). I'm not sure about the 'careful' bit.

'on the way out concluded' is the wordplay.
'on the way out' becomes 'going' (I've seen this before).
'concluded' becomes 'over' (synonyms).
'going'+'over'='GOING-OVER'

Can you help me to learn more?

(Another definition for going-over that I've seen is " Check, examination".)

I've seen this clue in The Guardian.

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