
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
Luke is borrowing $\$12{,}000$ from the bank. The bank offers him a choice between two $15$-year payment plans:

**Plan 1.** Luke's debt accumulates $8\%$ annual interest which compounds semi-annually. Luke pays off one-third of his balance after $5$ years, and the rest at the end of the $15$ years.

**Plan 2.** Luke's debt accumulates $8\%$ annual interest which compounds annually. Luke pays off his full balance at the end of the $15$ years.

Calculate the (positive) difference between Luke'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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