
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 garden is enclosed on three sides by a fence, with the fourth side against a long wall that is $500$ feet long. The fence costs $\$10$ per foot and $\$3,\!000$ altogether. Find the length of the side parallel to the wall that maximizes the area of the garden. Assume that at one corner of the garden, the fence forms a right angle.

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