I talk with LLMs for hours out of the day, every single day. I'm deeply familiar with their strengths and shortcomings on both a technical and intuitive level. I push them to their limits and have definitely witnessed novel output. The question remains, just how novel can this output be? Synthesis is a valid way to produce novel data.
And beyond that, we are teaching these models general problem-solving skills through RL, and it's not absurd to consider the possibility that a good enough training regimen cannot impart deduction/induction skills into a model that are powerful enough to produce novel information even via means other than direct synthesis of existing information. Especially when given affordances such as the ability to take notes and browse the web.