
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 \( ABC \) into \( n \) equal segments. Connect the division points with line segments parallel to each side. Find the total number of parallelograms formed within the network corresponding to its perimeter, denoted as \( f(n) \).

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