
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 construction company purchased an excavator at the beginning of the year for 1 million yuan and rents it to an engineering team for 220,000 yuan per year. The construction company is responsible for the maintenance of the excavator, with the first year's maintenance fee being 20,000 yuan. As the machine wears out, the maintenance cost increases by 20,000 yuan each subsequent year. Moreover, at the end of the x-th year (x ∈ N*, x ≤ 16), the machine can be sold for (80 - 5x) ten thousand yuan.
(1) Determine the function expression for the total profit y (in ten thousand yuan) the construction company makes by the end of the x-th year with respect to x (in years), and calculate its maximum value;
(2) To maximize the economic benefit, meaning to maximize the average annual profit, in which year should the construction company sell the excavator? Provide a rationale for your response.

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