
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 certain product has a cost price of $40 per unit and a selling price of $50 per unit. Each month, 210 units can be sold. For every $1 increase in the selling price per unit, 10 fewer units can be sold per month (the selling price cannot exceed $65 per unit). Let $x$ represent the dollar amount of increase in the selling price per unit (where $x$ is a positive integer) and $y$ represent the monthly sales profit.

1. Find the functional relationship between $y$ and $x$, and directly state the range of values for the independent variable $x$.
2. At what selling price per unit can the maximum monthly profit be achieved? What is the maximum monthly profit?

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