Crossword Genius

Nose about tuned-out Liberal, in a wise way (9)

Ross

I believe the answer is:

prudently

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'in a wise way' is the definition.
I can't tell whether this defines the answer.

'nose about tuned-out liberal' is the wordplay.
'nose' becomes 'pry' (to nose around is to pry).
'about' indicates putting letters inside.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'liberal' becomes 'l' (abbreviation).
'tuned' anagrammed gives 'udent'.
'udent'+'l'='udentl'
'pry' enclosing 'udentl' is 'PRUDENTLY'.

Can you help me to learn more?

(Other definitions for prudently that I've seen before include "Wisely" , "Carefully" , "Discreetly" .)

I've seen this clue in The Daily Express.
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