
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 certain car costs 169,000 yuan at the time of purchase. Each year, the total cost for insurance and gasoline is 9,000 yuan. The maintenance cost of the car is: 2,000 yuan in the first year, 4,000 yuan in the second year, 6,000 yuan in the third year, and so on, increasing by an arithmetic sequence each year.  
(1) Calculate the total cost (including the purchase cost) of using the car for 3 years.  
(2) Let the total cost (including the purchase cost) of using the car for $n$ years be $f(n)$. Write the expression for $f(n)$.  
(3) Determine after how many years it is most economical to scrap the car (i.e., after how many years the average cost is the lowest).

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