
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 congruent cones, each with a radius of 15 cm and a height of 10 cm, are enclosed within a cylinder. The bases of the cones are the bases of the cylinder, and the height of the cylinder is 30 cm. Determine the volume in cubic centimeters of the space inside the cylinder that is 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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