I don't know the answer to your question "how to build AGI". Although if I had to guess, the AGI will probably have a supervisor algorithm (trained by RL), which will issue internal commands to pattern matchers (like GPT-4), to drive them to solve the problem. The supervisor algorithm will only have a little tacit knowledge about any specific problem (like language or world facts), only tacit knowledge about learning and reasoning, and how to do it economically.

So the supervisor algorithm will do the tree search if needed.

Yes, but does it because it read somewhere? Can it adapt the existing solution to a new variation? Can it solve a similar problem with different things? This is what humans do all the time.