
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
An engineer invested $\$20,000$ in a six-month savings certificate that paid a simple annual interest rate of $8\%$. After six months, she reinvested the total value of her investment in another six-month certificate that now uses a compound interest formula, compounded monthly. After six more months, the investment was worth $\$21,735.60$. If the annual interest rate of the second certificate is $r\%$, then what is $r?$

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