
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
Determine all integers \( n \geqslant 2 \) with the following property: every \( n \) pairwise distinct integers whose sum is not divisible by \( n \) can be arranged in some order \( a_{1}, a_{2}, \ldots, a_{n} \) so that \( n \) divides \( 1 \cdot a_{1} + 2 \cdot a_{2} + \cdots + n \cdot a_{n} \).

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