Yes, that's what OpenAI o1 does, and DeepSeek R1. Also Google Gemini 2.0 Thinking models. It's a way to significantly improve benchmark scores, especially in math.
It's funny to watch too. I played with Gemini 2.0 on Google AI Studio and asked it to "come up with your favorite song as you take a long walk to really think this through".
The reasoning can then be shown, and it talked to itself, saying things like "since I'm an AI, I can't take walks, but with a request like this, the user seems to imply that I should choose something that's introspective and meaningful", and went on with how it picked candidates.
I just tried that prompt with gemini-2.0-flash-thinking-exp-01-21
In the reasoning process it concludes on:
From the brainstormed genres/artists, select a specific song. It's better to be concrete than vague. For this request, "Nuvole Bianche" by Ludovico Einaudi emerges as a strong candidate.
Craft the Explanation and Scenario: Now, build the response around "Nuvole Bianche."
Then in the actual answer it proposes:
"Holocene" by Bon Iver.