
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
If the sum of all positive divisors of a positive integer is twice the integer itself, it is called a perfect number. Find all positive integers \( n \) such that \( n-1 \) and \(\frac{n(n+1)}{2}\) are both perfect numbers.

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