
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
Divide each side of triangle \( \triangle ABC \) into \( n \) equal parts. Draw parallel lines through each of the division points parallel to the other two sides of the triangle. Determine the number of parallelograms formed by these parallel lines (which can also include the edges of the triangle).

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