
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 certain store sells a water product with a sales cost of $40 per kilogram. According to market analysis, if the selling price is set at $50 per kilogram, the store can sell 500 kilograms in a month. For every $1 increase in selling price, the monthly sales volume decreases by 10 kilograms. Given this situation with the water product, please answer the following questions:  
$(1)$ When the selling price is set at $55 per kilogram, calculate the sales volume and monthly sales profit.  
$(2)$ Let the selling price be $x$ dollars per kilogram and the monthly sales profit be $y$ dollars. Find the relationship between $y$ and $x$.  
$(3)$ If the store wants to ensure that the monthly sales profit reaches $8000 dollars without exceeding a monthly sales cost of $10000 dollars, what should the selling price be?

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