
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 store sells a small item with a cost price of $\\(2\\)$ yuan. According to market research, when the selling price is $\\(13\\)$ yuan, the average daily sales volume is $\(500\\)$ items. For every $\\(1\\)$ yuan decrease in the selling price, the store can sell an additional $\(100\\)$ items per day on average.

\\((1)\\) Let $y$ represent the profit and $x$ represent the selling price. Write the functional relationship between $y$ and $x$.

\\((2)\\) What is the selling price per item that maximizes the store's daily profit on this small item? What is the maximum profit?

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