
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 right cylinder with a height of 8 inches has a radius of 3 inches. A cone with the same radius but a height of 5 inches shares the base with the cylinder. What is the total surface area exposed to the outside (including the cylinder's curved surface, the cone's curved surface, and the base of the cone)?

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