
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
Given a cylinder with a diameter of 27 and a height of 30, contain two lead spheres with radii 6 and 9, with the larger sphere sitting on the bottom of the cylinder, calculate the volume of water required to just cover both spheres.

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