
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 rectangular cow pasture is enclosed on three sides by a fence and the fourth side is part of the side of a barn, which is $500$ feet long. However, only half of the barn’s length can be used for the pasture. The fence costs $\$7$ per foot, and the total budget for the fence is $\$1,\!470$. Determine to the nearest foot, 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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