
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 factory designed a craft with a cost of $20$ yuan per piece and put it on the market for trial sales. After investigation, the following data was obtained:

| Sales Price $x$ (yuan per piece) | $\ldots $ | $30$ | $40$ | $50$ | $60$ | $\ldots $ |
|----------------------------------|-----------|------|------|------|------|-----------|
| Daily Sales Volume $y$ (pieces)  | $\ldots $ | $500$| $400$| $300$| $200$| $\ldots $ |

$(1)$ It was found that the daily sales volume $y$ and the price $x$ satisfy a linear function relationship. Find the relationship between $y$ and $x$.

$(2)$ The local price department stipulates that the maximum selling price of the craft cannot exceed $45$ yuan per piece. What should be the selling price when the factory can make a profit of $8000$ yuan per day from the trial sales of the craft?

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