
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
For which \( n > 1 \) do there exist distinct natural numbers \( a_{1}, a_{2}, \ldots, a_{n} \) such that
$$
\operatorname{lcm}(a_{1}, a_{2}, \ldots, a_{n}) = a_{1} + a_{2} + \ldots + a_{n}
$$

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