
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 fishing company bought a fishing boat at the beginning of this year for 980,000 yuan for fishing. The first year requires various expenses of 120,000 yuan, and from the second year onwards, the annual expenses, including maintenance costs, increase by 40,000 yuan each year. The total fishing income of the boat is expected to be 500,000 yuan per year.  
(1) After how many years does the boat start to make a profit (i.e., the cumulative total income minus the cost and all expenses is positive)?  
(2) After fishing for several years, there are two options for handling the boat:  
① When the annual average profit reaches its maximum, sell the boat for 260,000 yuan;  
② When the cumulative total profit reaches its maximum, sell the boat for 80,000 yuan.  
Which option is more cost-effective? And explain the reason.

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