
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
Richard is planning to enclose a rectangular section of his yard using 500 feet of fencing. This enclosure is to cover three sides of the backyard, with his house forming the fourth side. Additionally, the length of the backyard must be twice the width. What is the maximum possible area for this backyard?

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