excogitate
To think over something carefully; to consider fully; cogitate.
The first organs which Gall excogitated, he placed in the region of the sinus; and it is manifest he was then in happy unacquaintance with everything connected with that obnoxious cavity.
To reach as a conclusion through reason or careful thought.
After many years of study, he excogitated a solution.
Where it comes from
From Latin excōgitāre, from ex- + cōgitāre (“think”).
Adapted from the Wiktionary entry excogitate (CC BY-SA 4.0).