
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 middle school agreed with a construction company to borrow 5 million yuan from the Construction Bank to build a student dormitory for a thousand people. The construction started at the beginning of 2010, was completed by the end of the year, and was put into use. The dormitory management decided to repay the Construction Bank loan (with an annual interest rate of 5%, calculated using compound interest) by collecting fees from students. After deducting 180,000 yuan for property management and utilities from the annual fees collected, the remaining amount is used to repay the loan at the end of each year.
(1) If the dormitory charges 800 yuan per student per year, in which year will the loan be fully repaid?
(2) If the dormitory management wants to repay the loan by the end of 2018, what is the minimum annual charge per student? (Round off to the nearest yuan.)

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