
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
Martin borrows $\$12{,}000$ from a bank. The bank offers him a choice between two $8$-year payment plans:

${\bf Plan~A.}$ Martin's debt accrues $8\%$ annual interest which compounds semi-annually. He pays off two-thirds of his balance after $4$ years, and the rest at the end of the $8$ years.

${\bf Plan~B.}$ Martin's debt accrues $8\%$ annual interest with **no compounding** (simple interest). He pays off his full balance at the end of the $8$ years.

Calculate the (positive) difference between Martin's total payments under Plan A and Plan B.

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