
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
Construct a fence around a rectangular field with an area of $s$ ($s>2.5$) square meters. In the center of the front wall, there must be an entrance that is 2 meters wide. The length of the rear wall must not exceed 20 meters. Given that the cost of constructing the rear wall is 45 yuan per meter, and the cost of other walls is 180 yuan per meter. Let the length of the rear wall be x meters, and denote the total cost of constructing the fence as $f(x)$ yuan.

(1) Find the expression for $f(x)$.
(2) Determine the value of x that minimizes the total cost of constructing the fence, and find the minimum total cost.

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