
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
The cost of constructing a new amusement park is 500,000 yuan, with an annual fixed cost (water, electricity, staff salaries, etc.) of 45,000 yuan. The annual maintenance cost is 10,000 yuan for the first year and increases by 10,000 yuan each subsequent year. How many years should the amusement park operate to minimize its average cost?

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