
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
Given a unique window design consisting of a rectangle with semicircles at each end, the ratio of $AD$ (the total length including semicircles) to $AB$ (diameter of the semicircles) is $4:3$. If $AB$ is 40 inches, calculate the ratio of the area of the rectangle to the combined area of the semicircles.

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