Search crate out (5)

I believe the answer is:
trace
'search' is the definition.
The answer and definition can be both related to thinking as well as being verbs in their base form.
Maybe they are linked in a way I don't understand?
'crate out' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'crate' is an anagram of 'TRACE'.
Can you help me to learn more?
(Other definitions for trace that I've seen before include "part of harness" , "Vestige, hint" , "Discover whereabouts" , "Detect - a small amount" , "Describe, small quantity" .)
