
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
College student village official Wang Shanliang implements the government's "targeted poverty alleviation" policy, helping the impoverished household of Zhang San purchase an energy-saving and environmentally friendly car for $90,000 for rental purposes. Assuming the first year's operating cost is $20,000, and from the second year onwards, the annual operating cost increases by $20,000 each year, and the car's annual operating income is $110,000. If the car is used for $n$ ($n\in\mathbb{N}^*$) years, and the annual average profit (profit equals income minus cost) reaches its maximum value, then $n$ equals \_\_\_\_\_\_.

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