
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The Devil offers a Human to play the following game. First, the Human pays a certain amount \( s \) and names 97 triples \(\{i, j, k\}\), where \(i, j, k\) are natural numbers not exceeding 100. Then, the Devil draws a convex 100-gon \( A_1 A_2 \ldots A_{100} \) with an area equal to 100, and pays the Human a prize equal to the sum of the areas of the 97 triangles \( A_i A_j A_k \). What is the maximum \( s \) at which it is beneficial for the Human to agree?

Present the answer in LaTex format: \boxed{Your answer}
user