
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
Two identical cones, each with a base radius of 15 cm and height of 15 cm, are perfectly enclosed within a cylinder such that the base of each cone conforms to one base of the cylinder and the tips of the cones meet at the center of the cylinder. The cylinder's height is 30 cm. Calculate the volume in cubic centimeters of the cylinder that is not occupied by the cones. Give your answer in terms of $\pi$.

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