
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 purchase price of 50 yuan per item and a selling price of 60 yuan per item, with a daily sales volume of 190 items. If the selling price of each item increases by 1 yuan, then 10 fewer items are sold each day. Let the selling price increase by $x$ yuan ($x$ is a positive integer), and the daily sales profit be $y$ yuan.

(1) Find the relationship between $y$ and $x$.

(2) At what selling price per item will the maximum daily profit be obtained? What is the maximum profit?

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