The chain of thought would be the final path through the tree. Interactively showing the thought tokens would give the game away, which is why they don’t show that.
In this case, the model would explore several chain of thoughts during training, but only output a single chain during inference (as the sibling comment suggests).
We can say the same thing about RL implying PPO, however there’s pretty big hints, namely Noam Brown being involved. Many of the things Noam Brown has worked on involve RL in tree search contexts.
He has also been consistently advocating the use of additional test-time compute to solve search problems. This is also consistent with the messaging regarding the reasoning tokens. There is likely some learned tree search algorithm, such as a learned policy/value function as in AlphaGo.
It’s all speculation until we have an actual paper. So we can’t categorically say MCTS/learned tree search isn’t involved.