
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
On each of the lines \( x=0 \) and \( x=2 \), there are 62 points marked with ordinate values \( 1, 2, 3, \ldots, 62 \). In how many ways can you choose three points from the marked 124 such that they form the vertices of a right triangle?

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