
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
Given a permutation \( s_0, s_2, \ldots, s_n \) of \( 0, 1, 2, \ldots, n \), we may transform it if we can find \( i, j \) such that \( s_i = 0 \) and \( s_j = s_{i-1} + 1 \). The new permutation is obtained by transposing \( s_i \) and \( s_j \). For which \( n \) can we obtain \((1, 2, \ldots, n, 0)\) by repeated transformations starting with \((1, n, n-1, \ldots, 3, 2, 0)\)?

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