Take out art at first in order to go through it carefully (4)

I believe the answer is:

sift

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'take' is the definition.
(I know that sift is a more specific form of the action take)

I can't explain the remainder of the clue.

Can you help me to learn more?

(Other definitions for sift that I've seen before include "screen" , "Sieve finely" , "Get lumps from (flour)" , "Remove lumps from, eg, flour" , "Sort carefully" .)

I've seen this clue in The Irish Times.

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