
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 exists a sequence \(\{x_{n}\}\) where \(1, 2, \cdots, n\) each appear exactly once and for \( k = 1, 2, \cdots, n \), \( k \) divides \( x_{1} + x_{2} + \cdots + x_{n} \).

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