
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
Given that \( p \) is a prime number and the set \( \mathrm{F}=\{0,1,2, \ldots, p-1\} \), if a subset \( \mathrm{A} \) of \( \mathrm{F} \) satisfies the condition that for any \( a, b \in A \), \( ab+1 \pmod{p} \in A \), then \( A \) is called a good set. Find the possible number of elements in a good set.

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