
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 Ganyu district, a bicycle-themed landscape boulevard has introduced 50 bicycles for tourists to rent. The cost of managing these bicycles is 125 yuan per day. Experience suggests that if the daily rental price per bicycle does not exceed 6 yuan, all bicycles can be rented out; however, if it exceeds 6 yuan, for each additional 1 yuan increase in rental price, 3 more bicycles will remain unrented. Given that the daily rental price per bicycle does not exceed 20 yuan, with increments of 2x yuan for whole numbers only, the total income generated by renting out all bicycles in one day must exceed the daily management costs. Let y represent the net income from renting out all bicycles for the day (i.e., the total income from renting out all bicycles for the day minus the management fees). 
(1) Determine the expression for the function f(x) and its domain;
(2) What should the daily rental price per bicycle be set at 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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