
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
Ben needs to borrow $10,000 from a bank, which offers him two options:
1. A twelve-year loan with an annual interest rate of 8% compounded monthly. After 6 years, Ben must pay half of what he owes, and the remainder will continue to accrue interest until the end of the twelve years.
2. A twelve-year loan with a simple annual interest rate of 9%. Ben will make a single lump-sum payment at the end of the twelve years.

Find the positive difference between the total amounts Ben has to pay back under the two loan options. Round your answer to the nearest dollar.

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