
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
Three congruent cones, each with a base radius of 14 cm and height of 14 cm, are enclosed within a cylinder. Each cone’s base coincides with a base of the cylinder, and two cones are stacked vertically at one base, while the third cone is inverted and occupies the opposite base. The height of the cylinder is 35 cm. 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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