
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 cylindrical barrel with radius \(3\) feet and height \(8\) feet is full of water. A solid cube with a side length of \(6\) feet is set into the barrel so that one edge of the cube is vertical. Calculate the volume \(v\) of water displaced by this cube.

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