
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
To account for both social and economic benefits, a certain region invests in ecological construction to further develop its tourism industry. According to the plan, an initial investment of 8 million yuan will be made this year, and the investment will decrease by $\frac{1}{5}$ every subsequent year. The estimated income from tourism this year is 4 million yuan, and due to the promotional effect of the construction on tourism, it is expected that the income will increase by $\frac{1}{4}$ every year thereafter.

(1) Let $a_n$ represent the total investment in yuan over n years (with the current year as the first year), and let $b_n$ represent the total income from tourism in yuan over n years. Write expressions for $a_n$ and $b_n$.

(2) How many years will it take at least for the total income from tourism to exceed the total investment?

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