
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
Samantha borrows $12,000 from a bank. The bank offers her a choice between two 8-year payment plans:

**Plan 1.** Samantha's debt accumulates 8% annual interest which compounds semi-annually. She pays off one-third of her balance after 4 years, and the rest at the end of 8 years.

**Plan 2.** Samantha's debt accumulates 8% annual interest which compounds annually. She pays off her full balance at the end of 8 years.

What is the (positive) difference between Samantha'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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