
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 transportation company has purchased a batch of luxury buses for passenger transport. According to market analysis, the total profit per bus, represented as $y$ (in ten thousand dollars), is related to the number of years of operation $x (x \in N^*)$ by the formula $y=-x^2+18x-36$.

(1) How many years should each bus be operated to maximize its total profit? Calculate the maximum total profit.
(2) How many years should each bus be operated to maximize its average annual profit? Calculate the maximum average annual profit.

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