
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 5 points on a plane, with lines connecting these points that are neither parallel, perpendicular, nor coincident. What is the maximum number of intersection points of the perpendicular lines drawn from each of the 5 points to the lines connecting the remaining 4 points? The 5 given points are not counted among the intersection points.

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