Where does the search prompt actually go in the initial prompt?

[brando90]

I noticed the initial prompt in the example does not contain the later suggested prompt i.e.,

initial_prompt = """


Input: 2 8 8 14
Possible next steps:
2 + 8 = 10 (left: 8 10 14)
8 / 2 = 4 (left: 4 8 14)
14 + 2 = 16 (left: 8 8 16)
2 * 8 = 16 (left: 8 14 16)
8 - 2 = 6 (left: 6 8 14)
14 - 8 = 6 (left: 2 6 8)
14 /  2 = 7 (left: 7 8 8)
14 - 2 = 12 (left: 8 8 12)
Input: use 4 numbers and basic arithmetic operations (+-*/) to obtain 24 in 1 equation
Possible next steps:
"""

does not contain

"Three experts with exceptional logical thinking skills are collaboratively answering a question using the tree of thoughts method. Each expert will share their thought process in detail, taking into account the previous thoughts of others and admitting any errors. They will iteratively refine and expand upon each other's ideas, giving credit where it's due. The process continues until a conclusive answer is found. Organize the entire response in a markdown table format. The task is:

So I'm confused. How is the model suppose to be used? Can this be clarified?