
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
Suppose a rectangle and a circle intersect so that each long side of the rectangle contains a chord of the circle, with each chord equal in length to twice the radius of the circle. If the width of the rectangle equals the diameter of the circle, calculate the ratio of the area of the rectangle to the area of the circle. Express your answer as a common fraction in terms of $\pi$.

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