
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
Kai walks around a rectangular track twice daily. Each long side of the rectangle is adjacent to a quadrant, forming a shape with two straight parts and one full circle ends. The track width varies — $4$ meters on one end and $8$ meters on the other. Kai notes it takes him $180$ seconds longer to walk two laps on the outside than on the inside. Determine his walking speed in meters per second.
A) \( \frac{\pi}{30} \) 
B) \( \frac{\pi}{15} \)
C) \( \frac{2\pi}{15} \)
D) \( \frac{\pi}{7.5} \)

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