If someone asks you to make a difficult decision — like what to have for dinner — it might lead to rumination, or a long period of deep thought.
Use the noun rumination when there's thoughtful consideration going on. If your grandfather answers every question by saying, "Hmm. Let me think about that," he is a fan of rumination. It comes from the verb ruminate, which means "to think deeply," but also means "to chew the cud." Both words come from the Latin word ruminatus, which has the same meaning and which is rooted in rumen, or "gullet."