
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
Private cars have a system for applying for scrapping. A car owner spends 150,000 yuan to purchase a vehicle, and the annual cost for insurance, tolls, and gasoline is about 15,000 yuan. The annual maintenance cost forms an arithmetic sequence with a common difference of 3,000 yuan, with the first year's maintenance cost being 3,000 yuan. The best number of years to apply for vehicle scrapping (the number of years with the lowest average annual cost) is ______ years.

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