reasoned

(verb) decide by reasoning; draw or come to a conclusion. Synonyms: reason, reason out, conclude. Example: "We reasoned that it was cheaper to rent than to buy a house."

(verb) present reasons and arguments. Synonyms: argue, reason.

(verb) think logically. Synonyms: reason. Example: "The children must learn to reason."

(adj) logically valid. Synonyms: sound, well-grounded. Example: "A sound argument."