
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
Beth needs to borrow $\$15,\!000$ from the bank. The bank offers her a single option:
A fifteen-year loan with an annual interest rate of $8\%$ compounded semi-annually. After 8 years, Beth must make a payment equal to one-third of the balance owed at that time. The remaining balance will continue to accrue interest, and the full amount is due at the end of 15 years.

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