
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 market survey shows that for a certain product, its sales volume decreases by 10 units for every 1 yuan increase in price above the cost price. Given that the cost price of this product is 40 yuan/unit, and 500 units can be sold at a price of 50 yuan/unit.
(1) Write the functional relationship between the selling price x (x > 40) yuan and the profit y yuan;
(2) Calculate the selling price that yields the maximum profit and find the maximum profit.

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