
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 any sequence, the following operation can be performed: each time select three consecutive terms in the sequence, denoted as \(a, b, c\), and replace them with \(b, c, a\), while keeping the other terms unchanged. Determine all integers \(n \geq 3\) for which the sequence \(1, 2, \cdots, n\) can be transformed into \(n, n-1, \cdots, 1\) through a finite number of operations.

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