Thought logically about a red nose (8)
I believe the answer is:
reasoned
'thought logically' is the definition.
('reason' can be a synonym of 'think logically')
'about a red nose' is the wordplay.
'about' indicates anagramming the letters.
'a'+'red'+'nose'='arednose'
'arednose' anagrammed gives 'REASONED'.
(Other definitions for reasoned that I've seen before include "Based on logic" , "Argued logically" , "Worked out through logic and sense" , "Argued, concluded" , "made a logical case" .)