
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
Olivia is considering borrowing $15,000$ from a bank. The bank offers her a choice between two 10-year payment plans:

${\bf Plan~1.}$ Olivia's debt gathers $8\%$ annual interest, compounding semi-annually. She pays off one-third of her balance after 3 years, another third after 6 years, and the rest at the end of the 10 years.

${\bf Plan~2.}$ Olivia's debt accumulates $8\%$ annual interest, compounding annually. She pays off her entire balance at the end of the 10 years.

What is the (positive) difference between Olivia'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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