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

**Plan 1.** Dan's debt accumulates $10\%$ annual interest which compounds biannually. Dan pays off half his balance after $5$ years, one third of the remaining balance after $7$ years, and the rest at the end of the $10$ years.

**Plan 2.** Dan's debt accumulates $12\%$ annual interest which compounds annually. Dan pays off his full balance at the end of the $10$ years.

What is the (positive) difference between Dan'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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