
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
In a plane, there are four points. Among all the lines connecting any two of these points, no two lines coincide, are parallel, or are perpendicular. From each point, perpendicular lines are drawn to all the lines formed by connecting the other three points. Determine the maximum number of intersection points of these perpendicular lines.

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