
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
Live shopping is gradually becoming a part of people's lives. A certain e-commerce platform is live selling a small commodity with a cost price of $8$ yuan per item on a certain $APP$. If it is sold for $10$ yuan per item, $200$ items can be sold per day. Through market research, it was found that for each increase of $1$ yuan in the selling price of each item, the number of items sold per day decreases by $20$ items. Let the selling price of each small commodity be $x$ (yuan) and the daily sales volume be $y$ (items). <br/> $(1)$ Find the functional expression between $y$ (items) and $x$ (yuan); <br/> $(2)$ If the e-commerce platform sells each small commodity at a price not lower than the cost price and not higher than $15$ yuan to make a profit of $640$ yuan per day from selling the commodity, what should be the selling price of each small commodity?

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