
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
$L_{1}$ and $L_{2}$ are two parallel lines in a plane, with $m$ and $n$ points respectively $(m, n \geq 2)$. Each point on $L_{1}$ is connected to each point on $L_{2}$ with a line segment. Given that any three of these line segments do not intersect at a common point within the plane region $D$ between $L_{1}$ and $L_{2}$, find the number of different intersection points among these line segments.

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