
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 travel company has allocated 50 sightseeing cars in a scenic area for tourists to rent. It is assumed that each sightseeing car can be rented out at most once a day, and the daily rental fee $x (\text{in yuan})$ for each car is a multiple of 5. The operating rules observed daily are as follows: when $x$ does not exceed 100 yuan, all sightseeing cars can be rented out; when $x$ exceeds 100 yuan, for each increase of 5 yuan in the daily rental fee, one less sightseeing car will be rented out. It is known that the daily management fee for all sightseeing cars is 1100 yuan. (Note: Net income = Rental income - Management fee)  
$(1)$ When the daily rental fee $x$ is 135 yuan, the number of sightseeing cars that can be rented out is ______.  
$(2)$ Let the daily net income be $y$ yuan, write the functional relationship between $y$ and $x$.  
$(3)$ For how much is the daily rental fee per car when the daily net income is maximized?

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