
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
**Problem 6.** Let  $p>2$  be prime. Find the number of the subsets  $B$  of the set  $A=\{1,2,\ldots,p-1\}$  such that, the sum of the elements of  $B$  is divisible by  $p.$ 

*Ivan Landgev*

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