
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
What positive integer value should we assign to \( p \) for the fraction \( \frac{p+2}{p+1} \) to be an integer? - Find all integers \( N \) that have no prime factors other than 2 and 3, and which have the property that the number of divisors of \( N^2 \) is three times the number of divisors of \( N \).

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