
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
Given that the cost price of a product is 40 yuan per unit, with a selling price of 50 yuan per unit, 210 units are sold each month. For every 1 yuan increase in the selling price, the monthly sales volume decreases by 10 units (the selling price cannot exceed 65 yuan). Let's assume the selling price is increased by x yuan (x is a positive integer), and the monthly profit is y yuan.
(1) Establish the functional relationship between y and x, and directly state the range of the independent variable x.
(2) At what selling price per unit will the monthly maximum profit be achieved? What is the maximum monthly profit?

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