
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 around the perimeter of a rectangle whose area is 180. The length of one side of the rectangle is three times the length of the other side. Rounded to the nearest whole number, 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}
user