
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 five points in a plane, the lines connecting each pair of these points are neither parallel, perpendicular, nor coincident. From each of these points, we draw perpendiculars to all the lines formed by connecting the remaining four points in pairs. What is the maximum number of intersection points of these perpendiculars, excluding the given five points?

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