
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 circle lies within a rectangle and touches three of its edges. The area inside the circle equals the area inside the rectangle but outside the circle. What is the ratio of the length of the rectangle to its width?

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