
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 tourist area advocates for a low-carbon lifestyle and offers bicycle rentals. There are 50 bicycles available for rent, and the cost of managing these bicycles is 115 yuan per day. Based on experience, if the daily rental price per bicycle does not exceed 6 yuan, all bicycles can be rented out; if it exceeds 6 yuan, for every additional 1 yuan, 3 bicycles will not be rented out. For ease of settlement, the daily rental price per bicycle $x$ (in yuan) is an integer, and it is required that the total income from renting bicycles for one day must be higher than the daily management cost. Let $y$ (in yuan) represent the net income from renting bicycles for a day (i.e., the total income from renting bicycles for the day minus the management cost).  
(1) Find the expression for the function $y=f(x)$ and its domain;  
(2) What should the daily rental price per bicycle be set at to maximize the net income for a day?

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