Deduce why one's been dismissed? (6,3)

I believe the answer is:

reason out

'deduce why' is the definition.
'reason out' can be an answer for 'deduce'. I'm not certain of the 'why' bit.

'one's been dismissed?' is the wordplay.
'one's been' becomes 'reason' (I can't justify this - if you can you should give a lot more credence to this answer).
'dismissed?' becomes 'out' (I've seen this before).
'reason'+'out'='REASON OUT'

(Another definition for reason out that I've seen is " Think through".)

I've seen this clue in The Times.

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