Visit this link and click on the "Thought for 11m38s" text: https://chatgpt.com/share/693ca54b-f770-8006-904b-9f31a58518... - that will show you exactly what it spent those 11 minutes doing, most of which was executing Python code using the reportlab library to generate PDF files, then visually inspecting those PDF files and deciding to make further tweaks to the code that generates them.
Incredibly dumb question, but when they say this, what actually happens?
Is it using TeX? Is it producing output using the PDF file spec? Is there some print driver it's wired into?