
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
Sarah needs to borrow $12,000 from a local credit union. The credit union offers her two options:

1. A twelve-year loan with an annual interest rate of $8\%$ compounded semi-annually. After 6 years, Sarah must make a payment equal to a third of the amount she owes at that time. The remaining balance continues to accrue interest, and at the end of the twelve years, Sarah will pay off the remaining balance.

2. A twelve-year loan with a simple annual interest rate of $9\%$. After 6 years, Sarah must make a payment of $3,000. The remaining balance will then accrue simple interest for the next 6 years, with the total amount due at the end of the term.

Calculate the total amount Sarah has to pay back under both schemes and find the positive difference between the two totals. Round your answer to the nearest dollar.

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