Take your time and think things through logically. That's what it means to use ratiocination to solve a problem.
To correctly pronounce ratiocination say, "rat-ee-oh-seh-NA-shun." Ratiocination uses reason or logic to figure something out. It might involve determining probabilities, syllogisms, even mathematical formulas, or simply following all the steps in a process that you believe will lead you to the correct or best answer. Ratiocination is the opposite of taking a wild guess or just "going with your gut."