
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 company made a net profit of 5 million yuan in 2003. Due to aging equipment and other reasons, the company's production capacity will decline year by year. Without technical renovation, it is predicted that the net profit will decrease by 2 million yuan each year starting from this year. At the beginning of this year, the company invested 6 million yuan at once for technical renovation. It is predicted that excluding the funds for technical renovation, the profit for the nth year (with this year being the first year) will be 500(1+ $$\frac{1}{2^{n}}$$) million yuan (n is a positive integer).
(Ⅰ) Suppose that the cumulative net profit of the company for the first n years, without technical renovation, is A<sub>n</sub> million yuan, and after technical renovation, deducting the investment for technical renovation, is B<sub>n</sub> million yuan. Find the expressions for A<sub>n</sub> and B<sub>n</sub>.
(Ⅱ) According to the predictions, after how many years will the cumulative net profit of the company, following the technical renovation, exceed that without the renovation?

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