
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
Sonia needs to borrow $20,\!000 from the bank. The bank gives her two options:

1. A twelve-year loan with an annual interest rate of $8\%$ compounded semiannually, with a condition to pay half of what she owes at the end of 6 years. The remaining amount continues to accrue interest until the end of twelve years when the balance is paid off.
  
2. A twelve-year loan with a simple annual interest rate of $10\%$, where she needs to make a full lump-sum payment at the end of the term.

Find the positive difference between the total amounts Sonia 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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