
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
The perimeter of a particular rectangle is equal to the circumference of a particular circle. If the length of the rectangle is twice its width, what is 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}
user