
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 two parallel lines \(a\) and \(b\), points \(A_{1}, A_{2}, \ldots, A_{m}\) and \(B_{1}, B_{2}, \ldots, B_{n}\) are chosen respectively, and all segments of the form \(A_{i}B_{j}\) are drawn \( (1 \leq i \leq m, 1 \leq j \leq n) \). How many points of intersection will there be, given that no three of these segments intersect at the same point?

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