
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 car company purchased 4 buses, each costing 2 million yuan, for long-distance passenger transport. It is estimated that each bus will earn about 1 million yuan per year, and the annual expenses for each bus are about 160,000 yuan, with the expenses increasing by 160,000 yuan each year starting from the second year.
1. Write the function relationship between the total profit $y$ (in million yuan) of operating the 4 buses and the number of years $x$ ($x \in \mathbb{N}^*$) they are operated.
2. For how many years should the 4 buses be operated to maximize the average annual operating profit?

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