
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 10 cm and height of 15 cm, are enclosed within a cylinder that also contains a sphere. The base of each cone is part of a base of the cylinder, and the height of the cylinder is 30 cm. The sphere, which fits exactly between the two cones, has a diameter of 10 cm. Calculate the volume of space within the cylinder not occupied by either the cones or the sphere.

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