
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 all integers  $n$  satisfying  $n \geq 2$  and  $\dfrac{\sigma(n)}{p(n)-1} = n$ , in which  $\sigma(n)$  denotes the sum of all positive divisors of  $n$ , and  $p(n)$  denotes the largest prime divisor of  $n$ .

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