
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 its diameter equal to its height is inscribed in a right circular cone. The cone has a diameter of 16 and altitude 20. The axes of the cylinder and cone coincide. Find the radius of the cylinder, and then calculate the space left in the cone above the cylinder. Express your answer as a common fraction.

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