
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 piece of string fits exactly once around the perimeter of a rectangle whose length is twice its width, and the area of the rectangle is 200. What is the area of the largest circle that can be formed from the piece of string?

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