
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 with a cost price of $40$ yuan per kilogram. Through market research, it is found that the weekly sales quantity $y$ (in kilograms) of the product is a linear function of the selling price $x$ (in yuan per kilogram). Some data is given in the table below:

| Selling Price $x$ (yuan per kilogram) | $45$ | $60$ | $70$ | $75$ |
|---------------------------------------|------|------|------|------|
| Weekly Sales Quantity $y$ (kilograms) | $110$ | $80$ | $60$ | $50$ |

$(1)$ Find the expression for the function between $y$ and $x$;  
$(2)$ At what selling price per kilogram will the maximum profit be obtained per week? What is the maximum profit in yuan?

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