
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 hotel has 100 identical beds. According to past experience, when the bed price (i.e., the daily rent per bed) does not exceed 10 yuan, all beds can be rented out; when the bed price is higher than 10 yuan, for each increase of 1 yuan, 3 beds will be vacant. In order to achieve better returns, the hotel wants to set an appropriate price for the beds, with the following conditions: ① The bed price should be an integer multiple of 1 yuan for easy billing; ② The hotel's daily expense is 575 yuan, and the income from bed rentals must exceed expenses, and the higher the better. If x represents the bed price, and y represents the hotel's net income per day (i.e., income after deducting daily expenses),
(1) Express y as a function of x;
(2) Try to determine the bed price that meets both conditions above and maximizes net income.

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