
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 fleet of luxury coaches for passenger service. Market analysis indicates that the total profit $y$ (in ten thousand yuan) from operating each coach is related to the number of years $x$ (where $x$ is a positive integer) it has been in operation according to the equation $y = -x^2 + 18x - 36$.
(1) After how many years of operation will a coach yield the maximum total profit?
(2) After how many years of operation will a coach yield the maximum average annual profit?

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