
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
An integer is a perfect number if and only if it is equal to the sum of all of its divisors except itself. For example, 28 is a perfect number since \(28 = 1 + 2 + 4 + 7 + 14\).

Let \(n!\) denote the product \(1 \cdot 2 \cdot 3 \cdots n\), where \(n\) is a positive integer. An integer is a factorial if and only if it is equal to \(n!\) for some positive integer \(n\). For example, 24 is a factorial number since \(24=4!=1 \cdot 2 \cdot 3 \cdot 4\).

Find all perfect numbers greater than 1 that are also factorials.

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