
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 positive integers \( n \) such that there exist positive integers \( k \) (\( k \geq 2 \)) and positive rational numbers \( a_1, a_2, \ldots, a_k \) that satisfy: \( a_1 + a_2 + \cdots + a_k = a_1 a_2 \cdots a_k = n \).

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