
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 $n$ points ($n > 2$) on a plane, where no three points are collinear. For any two of these points, draw a line through them and mark the point among the remaining points that is closest to this line (it is known that this point is uniquely determined for any situation). What is the maximum number of marked points for a given $n$?

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