
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 \( n \) lines in a plane (\( n > 2 \)), none of which are parallel and no three of which are concurrent. It is known that the plane can be rotated around a point \( O \) by a certain angle \(\alpha < 180^{\circ}\), such that each line coincides with the original position of another line. Find all possible values of \( n \).

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