
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
In the plane, three lines and \( n \) points are depicted such that there are exactly two points on either side of each line (points lying directly on the line do not belong to either side). For which values of \( n \) is this possible?

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