First day draw out, then figure it out with reasoning (6)
I believe the answer is:
deduce
'figure it out with reasoning' is the definition.
I can't judge whether this definition defines the answer.
'first day draw out' is the wordplay.
'first day' becomes 'd' (1st letter of 'day').
'draw out' becomes 'educe' (synonyms).
'd'+'educe'='DEDUCE'
'then' acts as a link.
Can you help me to learn more?
(Other definitions for deduce that I've seen before include "Reason out (something)" , "Draw conclusions" , "Derive by reasoning" , "Infer like Sherlock" , "Solve by reasoning" .)