
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
Find the odd prime number \( p \) that satisfies the following condition: There exists a permutation \( b_1, b_2, \cdots, b_{p-1} \) of \( 1, 2, \cdots, p-1 \) such that \( 1^{b_1}, 2^{b_2}, \cdots, (p-1)^{b_{p-1}} \) forms a reduced residue system modulo \( p \).

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