
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 residential community advocates a low-carbon lifestyle and encourages environmentally friendly travel by providing bicycle rental services. The community has 40 bicycles available for residents to rent, with a daily management cost of 92 yuan. Based on experience, if the daily rental price of each bicycle does not exceed 5 yuan, then all the bicycles can be rented out. If it exceeds 5 yuan, for every additional 1 yuan in price, there are 2 fewer bicycles rented out. To facilitate settlement, the daily rental price x yuan of each bicycle is an integer. The function $f(x)$ represents the daily net income from renting bicycles (daily net income = total daily income from bicycle rental - management expenses).
(1) Find the explicit expression of the function $f(x)$ and its domain.
(2) What rental price should be set to maximize the daily net income?

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