As your initial statement set limits I will limit my reply. Historic attributes of GOD (the Judeo-Christian one) are: Omniscience (all knowing) Omnipotence (all powerful) Omnipresence (everywhere [and btw everyWHEN]) As omniscience is one of the defining attributes I would have to pick it before thinking. But you limited thinking to having a novel thought, not that process by which we continue our existence and interaction with our surroundings. If GOD is omniscient there is no new thought left to 'think'.