
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
Consider five points \(X_1, X_2, \cdots, X_5\) on a plane. These points are paired and connected with blue lines such that no two blue lines are either perpendicular or parallel. For each point \(X_i\) (where \(1 \leq i \leq 5\)), each blue line \(l\) that does not pass through \(X_i\) has a red line passing through \(X_i\) that is perpendicular to \(l\). What is the maximum number of intersections among all the red lines?

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