verb (used with object), ex·cog·i·tat·ed, ex·cog·i·tat·ing.
1. to think out; devise; invent.
2. to study intently and carefully in order to grasp or comprehend fully.
See more synonyms on Thesaurus.com
Origin: 1520–30; < Latin excōgitātus past participle of excōgitāre. to devise, invent, think out. See ex-, cogitate
Now YOU come up with a sentence (or fic? or graphic?) that best illustrates the word.