
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 factory, in order to expand its production scale, purchased a high-performance production line at the beginning of this year. The maintenance cost of the production line will increase year by year during its use. The maintenance cost in the first year is $40,000. From the second year to the seventh year, the maintenance cost increases by $20,000 each year compared to the previous year. Starting from the eighth year, the maintenance cost increases by 25% compared to the previous year.

(I) Let the maintenance cost of the production line in the $n$th year be $a_{n}$. Find the expression for $a_{n}$.

(II) If the average maintenance cost per year for the first $n$ years of the production line is greater than $120,000, the production line needs to be updated. Find the average maintenance cost per year for the first $n$ years of the production line and determine in which year at the beginning of the year the production line needs to be updated.

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