
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
There are 100 points on a coordinate plane. Let \( N \) be the number of triplets \((A, B, C)\) that satisfy the following conditions: the vertices are chosen from these 100 points, \( A \) and \( B \) have the same y-coordinate, and \( B \) and \( C \) have the same x-coordinate. Find the maximum value of \( N \).

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