I tried it with thinking mode and it seems like it spiraled wildly internally, then did a web search and worked it out.

https://chatgpt.com/share/68e3674f-c220-800f-888c-81760e161d...

AIUI, they generally do all of that at the beginning. Another approach, I suppose, could be to have it generate a second pass? Though that would probably ~double the inference cost.