
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
Let \( p \) be an odd prime, and \( s(M) \) denote the sum of all the elements in the set \( M \). For the non-empty subsets \( T \) of the set \( F = \{1, 2, \ldots, p-1\} \), if \( p \) divides \( s(T) \), find the number of such subsets \( T \).

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