
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 decides to borrow $12,000 from the bank. The bank offers him two options:
1. A twelve-year loan with an annual interest rate of 8% compounded semi-annually. At the end of 6 years, Alex must make a payment equal to one-third of what he owes. The remaining balance continues to accrue interest, and at the end of the twelve years, Alex will pay off the rest.
2. A twelve-year loan with a simple annual interest rate of 10%, with just one lump-sum payment at the end of twelve years.

Determine the positive difference between the total amounts Alex must pay back under these two options. Round your answer to the nearest dollar.

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