
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 a sequence, one can perform the following operation: select three adjacent terms  $a,b,c,$  and change it into  $b,c,a.$  Determine all the possible positive integers  $n\geq 3,$  such that after finite number of operation, the sequence  $1,2,\cdots, n$  can be changed into  $n,n-1,\cdots,1$  finally.

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