
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
In a cinema in Hui City with 100 seats, ticket prices are uniform. According to the cinema's operational experience, if each ticket is priced at no more than 10 yuan, all tickets can be sold. For every 1 yuan increase in the ticket price above 10 yuan, 3 fewer tickets will be sold. To maximize revenue, a suitable ticket price needs to be set, with the following basic conditions:  
① For ease of change-making and accounting, the ticket price should be an integer multiple of 1 yuan;  
② The cost of showing one movie in the cinema is 575 yuan, and the box office revenue must exceed this cost.  
Let x (yuan) denote the price per ticket, and y (yuan) represents the net income of the cinema for showing one film (after deducting the cost).  
(Ⅰ) Express y as a function of x and determine its domain;  
(Ⅱ) What should the ticket price be set at per ticket, under the conditions, to maximize the net income for screening a film?

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