
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
An original garden is shaped as a rectangle 40 feet long and 20 feet wide, and it is enclosed by a fence. To use the garden more efficiently, while adjusting only one side of the fence, the garden is reshaped into an equilateral triangle with the same perimeter. How many square feet does this change in shape increase the area of the garden?

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