
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 fruit store sells a type of fruit. The purchase price is $30$ yuan per kilogram. According to a survey, when the selling price is $40$ yuan per kilogram, the store can sell an average of $500$ kilograms per day. For every $1$ yuan increase in the selling price, the store sells $10$ kilograms less. Let the selling price be $x$ yuan.<br/>$(1)$ Express the sales volume $y$ in terms of the selling price $x$.<br/>$(2)$ If the store makes a profit of $8000$ yuan and aims to offer consumers affordable prices, what should be the price of the fruit?<br/>$(3)$ What is the maximum profit of the fruit store? What should be the selling price at that time?

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