
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
For two perpendicular lines \(a\) and \(b\) in a plane, \((a, b)\) is called a "perpendicular pair", and both \(a\) and \(b\) are lines belonging to this "perpendicular pair". Given that there are twenty lines in the plane, what is the maximum number of "perpendicular pairs" that can be formed?

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