
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 in a plane, none of the lines connecting these points pairwise are parallel, perpendicular, or coincident. From each of the given points, perpendicular lines are drawn to all the lines formed by connecting the remaining four points pairwise. What is the maximum number of intersection points of these perpendiculars, excluding the given 5 points?

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