
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 rental company owns 100 cars. When the monthly rent for each car is set at 3000 yuan, all cars can be rented out. For every 50 yuan increase in the monthly rent per car, there will be one more car that is not rented out. The rental company needs to spend 150 yuan on maintenance for each car that is rented out per month, and 50 yuan on maintenance for each car that is not rented out per month.  
(1) When the monthly rent for each car is set at 3600 yuan, the number of cars that can be rented out is ____, and the monthly income of the rental company is ____ yuan;  
(2) Let the monthly rent for each car be x yuan (x≥3000) and the monthly income of the rental company be y yuan, try to write the function relationship between y and x;  
(3) When the monthly rent for each car is set at how much yuan, will the rental company's monthly income be maximized? What is the maximum monthly income?

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