
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 is considering a loan of $15,000. The bank offers him two choices:
1. A fifteen-year loan with an annual interest rate of 8% compounded monthly, with a requirement that after 7 years, Alex must make a payment equal to half of the owed amount. The remaining balance continues to accrue interest until the end of the fifteen years when Alex will pay off the rest.
2. A fifteen-year loan with a simple annual interest rate of 10%, with a single payment at the end of the term.

Calculate the positive difference between the total amounts Alex has to pay back under each option. Round your answer to the nearest dollar.

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