
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 coastal tourism company purchased a yacht at the beginning of this year for 490,000 yuan and immediately put it into use. It is expected to generate an annual income of 250,000 yuan. In addition, there will be a certain maintenance cost every year. The maintenance cost for the first year is 40,000 yuan, and from the second year onwards, the maintenance cost will increase by 20,000 yuan each year. Let the profit after using the yacht for $x$ years be $y$ ten thousand yuan.  
(1) Write the function relationship between $y$ and $x$;  
(2) How many years should the yacht be used to maximize the average annual profit?

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