
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
Given that there are $m$ fixed points on the positive half of the $X$-axis and $n$ fixed points on the positive half of the $Y$-axis, connect each pair of these $m$ and $n$ points with a line segment. Assuming that no three segments intersect at the same point, determine the number of intersection points of all the connected line segments (not including the endpoints of the segments).

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