
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 a bank. The bank offers him a choice between two 15-year payment plans:

**Plan 1.** Luke's debt accumulates 8% annual interest which compounds quarterly. Luke pays off half his balance after 7.5 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, plus a fixed fee of $500.

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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