
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 company purchased a new piece of equipment at the cost of 90,000 yuan. The operation cost for the first year is 20,000 yuan, and from the second year onward, the annual operating cost increases by 20,000 yuan each year. Assuming the equipment is used for n (n ∈ N*) years, the annual income generated by the equipment is 110,000 yuan, and the annual average profit (profit being the income minus the cost) reaches its maximum value, find the value of n.

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