
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 farm uses one side of a $500$ feet long barn as part of the enclosure for a rectangular sheep pasture. The rest is enclosed with a fence that costs $\$5$ per foot. If the total cost of the fence is $\$1,\!500$, find the length of the side parallel to the barn that will maximize the area of the pasture.

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