Oh right you're very focused on specifically the strawberry problem. I just gave that as a throwaway example. It's a solution but not necessarily the solution for something that simple.
My point was much more general, that code execution is a key part of these models ability to perform maths, analysis, and provide precise answers. It's not the only way, but a key way that's very efficient compared to more inference for CoT.
there are multiple ways to disprove this
1. GPT o1 was released and it never supported the tools and it easily solved the strawberry problem - it was named strawberry internally
2. you can run GPT 5.2-thinking in the API right now and deny access to any tools, it will still work
3. you can run deepseek locally without tools and run it, it will still work
Overall this idea that LLM's cant reason and need tools to do that is misleading and false and easily disproven.