
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
A doctor invested $\$12,\!000$ in a six-month savings certificate that paid a simple annual interest rate of $10\%$. After six months, the total value of her investment was reinvested in another six-month certificate that compounded interest semi-annually. After the additional six months, the final investment was worth $\$13,\!260$. If the annual interest rate of the second certificate is $r\%$, what is $r$?

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