
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 circular cylinder with radius 3 externally tangents a hemisphere with radius 7 along one generatrix. If this setup is symmetric about the center of the hemisphere, and the base of the cylinder is parallel to the base of the hemisphere, determine the height of the cylinder. Also, find the total surface area of the cylinder.

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