
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 a plane with a given rectangular Cartesian coordinate system, a square is drawn with vertices at the points \((0, 0), (0, 65), (65, 65),\) and \((65, 0)\). Find the number of ways to choose two grid points inside this square (excluding its boundary) such that at least one of these points lies on one of the lines \(y = x\) or \(y = 65 - x\), but both selected points do not lie on any lines parallel to either of the coordinate axes.

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