
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 3000 yuan, all of them 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 maintenance cost for each rented car is 150 yuan per month, and for each car that is not rented out, the maintenance cost is 50 yuan per month. When the monthly rent per car is set to x yuan, the monthly income of the rental company is y yuan.
(1) Please write down the function relationship between x and y (no need to specify the domain).
(2) If the rental company rented out 88 cars in a certain month, how much is the monthly income of the rental company?

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