
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
Luke is borrowing $12{,}000 from the bank. The bank offers him a choice between two different $10$-year payment plans:
- **Plan 1:** Luke's debt accumulates 8% annual interest which compounds semi-annually. Luke pays off a third of his balance after 5 years, and the rest at the end of the 10 years.
- **Plan 2:** Luke's debt accumulates 8% annual interest which compounds annually. Luke pays off a third of his balance after 7 years, and the rest at the end of the 10 years.

What is the positive difference between Luke's total payments under Plan 1 and Plan 2? Round to the nearest dollar.

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