
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
Three congruent cones, each with a radius of 8 cm and a height of 8 cm, are enclosed within a cylinder. The bases of two cones are at each base of the cylinder, and one cone is inverted in the middle touching the other two cones at their vertices. The height of the cylinder is 16 cm. What is the cubic centimeters in the volume of the cylinder not occupied by the cones? Express your answer in terms of $\pi$.

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