
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 such that no two segments connecting any pairs of these points coincide, are parallel, or are perpendicular. How many intersection points can there be among the perpendiculars drawn from each point to the connecting segments between the other points, excluding the 5 given points?

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