
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
Use a 32-meter-long fence to enclose a rectangular chicken coop, with one side of the rectangle being $x$ meters long and the area being $y$ square meters.  
(1) Find the function relationship of $y$ with respect to $x$;  
(2) What should be the value of $x$ when the area of the enclosed chicken coop is 60 square meters?  
(3) Is it possible to enclose a chicken coop with the maximum area? If so, find the side length and the maximum area; if not, explain why.

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