
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 an integer $n$, such that there exist natural number $k \geqslant 2$ and positive rational numbers $a_{1}, a_{2}, \cdots, a_{k}$, satisfying
$$
a_{1}+a_{2}+\cdots+a_{k}=a_{1} a_{2} \cdots a_{k}=n .
$$

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