
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 company invests $100 million to purchase a set of equipment. The annual operating cost of the equipment is $0.5 million, and a certain amount of maintenance fee is required each year. The maintenance fee in the first year is $2 million, and due to equipment aging, the maintenance fee increases by $2 million each year. To minimize the average annual cost of the equipment, the number of years the company needs to update the equipment is ________.

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