
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]


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Given an arithmetic sequence of integers \(a_{1}, a_{2}, \cdots, a_{n}(n \geq 2)\) that satisfies \(k \mid a_{k} (k=1,2, \cdots, n-1)\) and \(n \nmid a_{n}\), determine all possible values of the positive integer \(n\).

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