
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 type of production equipment costs \\($10\\) ten thousand dollars at the time of purchase, with an annual management fee of \\($9\\) thousand dollars. The maintenance costs for this equipment in each year are: \\($2\\) thousand in the first year, \\($4\\) thousand in the second year, \\($6\\) thousand in the third year, and increasing by \\($2\\) thousand each year thereafter. What is the maximum number of years this equipment can be used before it should be decommissioned for optimal cost-effectiveness (i.e., when the average annual cost is minimized)?

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