
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 $15,000 from the bank. The bank offers him a choice between two 12-year payment plans:

**Plan 1.** Luke's debt accumulates 8% annual interest which compounds semi-annually. Luke pays off half his balance after 6 years, and the rest at the end of the 12 years.

**Plan 2.** Luke's debt accumulates 8% annual interest which compounds annually. Luke pays off his full balance at the end of the 12 years.

What is 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}
user