
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
Jenny is deciding between two $10$-year loan repayment plans for borrowing $\$12,000$ from the bank:

**Plan 1.** Jenny's debt grows with a $5\%$ annual interest rate that compounds monthly. She decides to pay off half her balance after $5$ years and address the remainder at the end of $10$ years.

**Plan 2.** Jenny's debt grows with a $3\%$ annual interest, compounding annually. She will settle the full balance at the end of the $10$ years.

What is the (positive) difference between Jenny's total payments under Plan 1 and Plan 2? Provide your answer rounded to the nearest dollar.

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