
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 a prime number \( p \) that satisfies the following conditions: there exist positive integers \( n, u, v \), such that the number of positive divisors of \( n \) is equal to \( p^{\mu} \), and the sum of these \( p^{2} \) positive divisors is equal to \( p^{*} \). Find all possible values of \( p \).

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