
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 unit decided to invest 3200 yuan to build a warehouse (in the shape of a rectangular prism), with a constant height. The back wall uses an old wall at no cost, the front is made with iron bars at a cost of 40 yuan per meter, the two side walls are made of bricks at a cost of 45 yuan per meter, and the roof costs 20 yuan per square meter.  
(1) Let the length of the iron bars be $x$ meters, and the length of one brick wall be $y$ meters, find the expression for the function $y=f(x)$.  
(2) To maximize the total surface area $S$ of the warehouse, how long should the front iron bars be designed? And what is the maximum value of $S$?

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