
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
Given a hemisphere of radius 9 cm sitting on a cone of height 12 cm, where the radius of the cone's base is the same as the hemisphere's radius, calculate the total surface area, including the hemisphere's rounded surface, base, and the lateral surface area of the cone. Express your answer in terms of $\pi$.

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