
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 decision has been made by the Sichuan Wenchuan Earthquake Command to construct a batch of simple houses (the shape of the house is rectangular, with a height of 2.5 meters). The front and back walls use 2.5-meter high color steel plates, and the two sides use 2.5-meter high composite steel plates. The price of both types of steel plates is calculated based on their length (i.e., the height of the steel plates is uniformly 2.5 meters, and the price of the steel plate is calculated as the length of the steel plate multiplied by the unit price). The unit price per meter is: 450 yuan for color steel plates and 200 yuan for composite steel plates. The roof is constructed using other materials, with a material cost of 200 yuan per square meter. The material cost for each house is controlled within 32,000 yuan.
(1) Let the length of the front wall of the house be x, the length of the two side walls be y, and the material cost be p. Express p in terms of x and y.
(2) What is the maximum area of the simple house? Also, find the length of the front wall when the area is maximum.

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