
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 a height of 15 cm, are enclosed within a cylinder. The base of each cone is a base of the cylinder, and the height of the cylinder is 35 cm. A sphere with a radius of 5 cm is also placed in the cylinder, centrally on one of the cone's apex. What is the number of cubic centimeters in the volume of the cylinder not occupied by the cones and the sphere? Express your answer in terms of \(\pi\).

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