
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
Since December 4, 2017, Zhengzhou has implemented an odd-even license plate restriction for motor vehicles, but new energy vehicles are not subject to this restriction. To facilitate travel, someone plans to purchase a new energy vehicle. Assuming the cost of purchasing the car is 144,000 yuan, the annual insurance, charging, and other fees total 9,000 yuan, and the maintenance cost of the car is: 2,000 yuan for the first year, 4,000 yuan for the second year, 6,000 yuan for the third year, and so on, increasing annually in an arithmetic sequence.
​(1) Let the total cost of using the car for \(n\) years (including the purchase cost) be \(f(n)\), try to write the expression for \(f(n)\);

(2) How many years should this new energy vehicle be used before it is scrapped to be the most cost-effective (i.e., the minimum average annual cost), and what is the minimum value of the average annual cost?

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