
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
For any non-empty finite set \( A \) of real numbers, let \( s(A) \) be the sum of the elements in \( A \). There are exactly 613 subsets \( A \) of \(\{1, \ldots, 23\}\) with 3 elements such that \( s(A)=36 \). Find the number of 3-element subsets of \(\{1, \ldots, 23\}\) with \( s(A)<36 \).

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