
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 fruit supermarket purchases a batch of cherries at a price of 20 yuan per kilogram. It is stipulated that the selling price of cherries per kilogram should not be lower than the purchase price and not higher than 40 yuan. A market survey found that the daily sales volume y (in kilograms) of cherries satisfies a linear function relationship with the selling price x (in yuan) per kilogram. Some corresponding data is shown in the table below:

| Selling Price (yuan per kilogram) | ... | 25 | 30 | 35 | ... |
|-----------------------------------|-----|----|----|----|-----|
| Daily Sales Volume (kilograms)    | ... | 110| 100| 90 | ... |

(1) Find the functional relationship between y and x.  
(2) If the supermarket wants to make a daily sales profit of 1000, how much should the selling price per kilogram of cherries be?  
(3) When the selling price per kilogram of cherries is set at what price, the daily sales profit is maximized? What is the maximum profit?

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