
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 \( x=2 \) and \( x=9 \), there are 400 points marked with ordinates \( 1, 2, 3, \ldots, 400 \). In how many ways can three points be chosen from the 800 marked points so that they form the vertices of a right triangle?

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