
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
Tamara needs to borrow $\$15,\!000$ from the bank. The bank offers her two options:

1. A fifteen-year loan with an annual interest rate of $8\%$ compounded semi-annually, with the condition that at the end of 7 years, Tamara must make a payment equal to half of what she owes. The remaining balance will continue to accrue interest, and at the end of the fifteen years, Tamara 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.

Find the positive difference between the total amounts Tamara has to pay back under the two schemes. Round your answer to the nearest dollar.

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