
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 purchased a batch of luxury coaches for passenger transportation. According to market analysis, the total profit \\(y\\) in ten thousand yuan of operating each bus is related to the number of years \\(x\\) it has been in operation \\(x \in \mathbb{N}^*\) as \\(y = -x^2 + 18x - 36\).
\\((1)\\) How many years should each bus operate to maximize its total profit? Calculate the maximum total profit.
\\((2)\\) After how many years of operation can each bus achieve the maximum average annual profit? Calculate the maximum average annual profit.

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