
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 new type of car costs \\(10\\) ten thousand yuan to purchase, with annual insurance, road maintenance, and fuel costs approximately \\(0.9\\) ten thousand yuan. The maintenance cost for the first year is \\(0.2\\) ten thousand yuan, increasing by \\(0.2\\) ten thousand yuan each subsequent year. What is the number of usage years that minimizes the car's average annual cost?

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