
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 site has 50 bicycles available for rent, and the daily management cost for these bicycles is 115 yuan. According to experience, if the daily rent for each bicycle does not exceed 6 yuan, all the bicycles can be rented out; if it exceeds 6 yuan, for every 1 yuan increase, 3 more bicycles remain unrented. The daily rent for each bicycle should not exceed 20 yuan, the daily rent $x$ yuan for each bicycle must be an integer, and the total income from renting all the bicycles in one day must exceed the daily management cost. Let $y$ represent the net daily income from renting all bicycles (i.e., the total income from renting all the bicycles in one day minus the management cost).  
(1) Find the analytical expression and domain for the function $y=f(x)$.  
(2) What should the daily rent for each bicycle be to maximize the daily net income? What is the maximum daily net income?

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