
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 decorative window consists of a rectangle and a semicircle at each end. If the ratio of the length `AD` of the rectangle to its width `AB` is `3:1`, and `AB` is 40 inches, what is the ratio of the area of the rectangle to the combined area of the semicircles? Additionally, calculate the total area of the window.
**A)** $\frac{12}{\pi}$, **B)** $\frac{9}{\pi}$, **C)** $12:\pi$, **D)** $4800 + 400\pi$, **E)** $\frac{8}{\pi}$

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