
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
The dimensions of a truncated cone are such that a sphere with a center at the center of the larger base and which touches the plane of the smaller base also touches the lateral surface. We know that the volume of the hemisphere that fits into the truncated cone is $6 / 7$ of the volume of the truncated cone.

What is the ratio of the lateral surface area of the truncated cone to the surface area of the hemisphere?

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