
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 cylinder has a radius of 10 cm and a height of 30 cm. Within this cylinder, a full cone with the same base as the cylinder and a height of 10 cm is placed at one base. Another cone, with the same dimensions, has only half of its volume inside the cylinder from the other base. What is 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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