
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 four points on a plane, any two lines connecting these points are neither coincident, parallel, nor perpendicular. Find the maximum number of intersection points of the perpendiculars drawn from each point to all lines formed by connecting the other three points.

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