
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 to purchase. Each year, a total of 10,000 yuan is paid for insurance and gasoline; the maintenance cost of the car in the first year is 1,000 yuan, and it increases by 2,000 yuan every subsequent year.
(Ⅰ) Let $S_n$ represent the total cost (including the purchase cost) after using the car for $n$ years. Derive an expression for $S_n$.
(Ⅱ) Determine the number of years for which using the car and then scrapping it is most economical (i.e., the number of years after which the average cost is minimized).

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