Since I used this one recently, I thought it wise to include it.

ratiocinate (ra·ti·oc·i·nate): / rash ee OS uh nayt /
intransitive verb

(1) to reason methodically; to think or argue logically

[From Latin ratiocinatus, past participle of ratiocinari meaning “to reckon, compute, calculate, conclude,” from Latin ratio meaning “calculation.”]

Usage: The debate team could not ratiocinate their position in the time allotted; therefore, they lost the tournament.