
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 farmer builds a rectangular chicken coop that leans against a wall, covering an area of 36m<sup>2</sup>. Due to geographical constraints, the length of the side of the chicken coop, $x$, cannot exceed 7m. The wall height is 2m. The cost of constructing the front of the chicken coop is 40 yuan/m<sup>2</sup>, the cost of constructing the side is 20 yuan/m<sup>2</sup>, and the total cost for the ground and other expenses is 1800 yuan.  
(1) Express the total cost $y$ as a function of $x$, and state the domain of this function.  
(2) What should be the length of the side to minimize the total cost? What is the minimum total cost?

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