
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
A square is drawn on a plane with a given rectangular Cartesian coordinate system, with vertices at points \((0, 0)\), \((0, 69)\), \((69, 69)\), and \((69, 0)\). Find the number of ways to choose two lattice points inside this square (excluding its boundary) such that at least one of these points lies on one of the lines \(y = x\) or \(y = 69 - x\), but neither of the chosen points lies on any line parallel to the coordinate axes.

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