
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 cinema has 1000 seats, and the price of tickets is fixed regardless of seat location. Based on the cinema's operating experience, if the price of each ticket does not exceed 10 yuan, all tickets can be sold out; when the ticket price is higher than 10 yuan, for every additional 1 yuan increase in price, 30 seats will remain unsold. In order to achieve better revenue, a suitable ticket price must be determined for the cinema. The basic conditions are: (1) For convenience in making change and accounting, the ticket price is set as an integer multiple of 1 yuan; (2) The cost of showing a movie at the cinema is 5750 yuan, and the box office revenue must exceed this cost. Use $x$ (in yuan) to represent the price of each ticket, and $y$ (in yuan) to represent the net income (income after removing costs) from showing a movie once. (I) Find the analytic expression for the function $y=f(x)$. (II) What ticket price should be set so that the net income from showing a movie is maximized?

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