
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
Given that \( n \) is a positive integer. If there exist integers \( a_{1}, a_{2}, \cdots, a_{n} \) (not necessarily distinct) such that \( a_{1} + a_{2} + \cdots + a_{n} = a_{1}a_{2} \cdots a_{n} = n \), then \( n \) is called "fascinating". Find all fascinating integers.

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