
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
Determine all pairs  $ (n,p)$  of positive integers, where  $ p$  is prime, such that  $ 3^p\minus{}np\equal{}n\plus{}p$ .

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