
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 rectangle ABCD is given. On the side AB, \( n \) different points are chosen strictly between A and B. Similarly, \( m \) different points are chosen on the side AD between A and D. Lines are drawn from the points parallel to the sides. How many rectangles are formed in this way?

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