
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
In a rectangle, a segment \( AB \) of length \( l = 4 \), which is less than the lengths of its sides, is positioned such that the endpoints of the segment lie on the sides of the rectangle. Point \( A \), making a full revolution around the rectangle, travels a distance equal to its perimeter. During this motion, point \( C \), the midpoint of segment \( AB \), also traces out a certain path. By how much is this path shorter than the perimeter of the rectangle?

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