
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
After the completion of a city's subway system, including platforms and other ancillary facilities, the average investment cost per kilometer is 100 million RMB. The entire investment is borrowed from the bank. Starting from the year the subway begins operation, the subway company must repay the bank an equal amount of the loan principal, which is 0.05 billion RMB per year. This loan principal is first paid with the subway's operating income, and any shortfall is supplemented by the municipal government from public funds. After the subway begins operation, the average annual operating income per kilometer (after deducting expenses such as daily management fees) is 0.0124 billion RMB in the first year, and it increases by 20% each year thereafter, with no increase after the 20th year. Find:  
(1) After how many years of operation does the subway's annual operating income begin to exceed the annual repayment of the bank loan principal?  
(2) Up to the year when the annual operating income exceeds the annual repayment of the bank loan principal, how much has the municipal government cumulatively paid for 1 kilometer of the subway?  
(Precise to the yuan, 1 billion = 1×10<sup>8</sup>)

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