
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 with a height of 36 cm and a radius of 10 cm contains three identical cones, each with a height of 18 cm and a radius of 10 cm. The cones are placed such that their vertices point downwards and their bases are each one-third the base of the cylinder. Calculate the volume of the space in the cylinder not occupied by the cones, expressing your answer in terms of \(\pi\).

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