
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 supermarket sells a small commodity with a cost price of $3.5$ yuan. According to market research, when the selling price is $14.5$ yuan, the average daily sales volume is 500 units. For every $1$ yuan decrease in the selling price, an additional 100 units can be sold daily.

(1) Assuming each item is reduced in price by $x$ yuan, let $y$ yuan be the profit the store makes from selling this item daily. Write the relationship between $y$ and $x$.

(2) At what selling price per item does the supermarket make the maximum profit from selling this item daily? What is the maximum profit?

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