
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
For a certain product, the cost price per item is $80$ yuan, and the selling price is $100$ yuan. $100$ items are sold per day. If the selling price is reduced by $x$ percent ($1$ percent $=10\%$), the quantity of goods sold will increase by $\frac{8}{5}x$ percent. The selling price must not be lower than the cost price.

$(1)$ Let the daily turnover of the store be $y$. Try to find the function relationship between $y$ and $x$, $y=f(x)$, and state its domain;

$(2)$ If it is further required that the daily turnover of the product must be at least $10260$ yuan, find the range of values for $x$.

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