
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
Straw returning to the field is a widely valued measure for increasing soil fertility and production in the world today, which eliminates the air pollution caused by straw burning and also has the effect of increasing fertility and production. A farmer spent $137,600 to buy a new type of combine harvester to achieve straw returning to the field while harvesting. The annual income from harvesting is $60,000 (fuel costs deducted); the harvester requires regular maintenance, with the first year's maintenance being free of charge provided by the manufacturer, and from the second year onwards, the farmer pays for the maintenance, with the cost $y$ (in yuan) related to the number of years $n$ used as: $y=kn+b$ ($n\geqslant 2$, and $n\in N^{\ast}$), knowing that the second year's maintenance costs $1,800 yuan, and the fifth year's costs $6,000 yuan.  
(Ⅰ) Try to find the relationship between the maintenance cost $f(n)$ (in yuan) and the number of years $n$ ($n\in N^{\ast}$) used;  
(Ⅱ) How many years should this harvester be used to maximize the average profit? (Profit = Income - Maintenance cost - Cost of machinery)

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