
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, where the lines connecting any two of these points are neither parallel, nor perpendicular, nor coincident. For each point, draw lines perpendicular to the lines connecting it to the other four points. What is the maximum number of intersection points of these perpendicular lines (excluding the given 5 points)?


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