
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
Alex needs to borrow $15,000 from the bank. The bank offers him two options:

1. A fifteen-year loan with an annual interest rate of $8\%$ compounded monthly. At the end of 10 years, Alex must make a payment equal to half of what he owes at that time. The remaining balance will continue to accrue interest, and at the end of fifteen years, Alex will pay off the remaining balance.

2. A fifteen-year loan with a simple annual interest rate of $10\%$, with just one lump-sum payment at the end of the fifteen years.

Calculate the total amount Alex has to pay back under each scheme and find the positive difference. Round your answer to the nearest dollar.

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