
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
Sarah is borrowing $\$15,000$ from the bank. The bank offers a choice between two $10$-year payment plans:

${\bf Plan~1.}$ Sarah's debt accumulates $10\%$ annual interest that compounds semiannually. Sarah pays off a third of her balance after $5$ years, and the rest at the end of the $10$ years.

${\bf Plan~2.}$ Sarah's debt accumulates $10\%$ annual interest which compounds annually. Sarah pays off a quarter of her debt after 5 years and the remaining balance at the end of 10 years.

What is the (positive) difference between Sarah'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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