ratiocinate
To use the powers of the mind logically and methodically; to reason.
intransitive, transitive
"Observe the relative position," returned the Doctor with a smile. "It is your attitude to believe through thick and thin in one man's judgment—your own. I follow the same opinion, but critically and with open eyes. Which is the more irrational—I leave it to yourself." "Oh, my dear fellow!" cried Casimir, "[…] don't ratiocinate with me."
Where it comes from
From Latin ratiōcinor (“to reckon, argue”) + -ate, from ratiō + -cinor. First use appears c.1643 in the writings of Kenelm Digby.
Adapted from the Wiktionary entry ratiocinate (CC BY-SA 4.0).