
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 family sedan incurs the following expenses over x years of use: an initial purchase cost of 120,000 yuan; insurance, road maintenance, fuel, and other various fees of 10,500 yuan per year; maintenance costs totaling 0.05x<sup>2</sup>+0.15x thousand yuan; after x years of use, the value of the sedan is (10.75-0.8x) thousand yuan. If the annual average expenditure on this family sedan is y thousand yuan, then based on the above conditions, solve the following questions:  
(1) Write the function relationship of y with respect to x;  
(2) Determine after how many years of using the family sedan the annual average expenditure is the lowest. Also, calculate this minimum expenditure.

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