
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 container with a radius of 5 feet and a height of 12 feet is filled with water. A solid cube with each side of length 6 feet is dropped into the cylinder such that the cube's diagonal is vertically aligned. We need to calculate the volume of water $v$ displaced by the cube in cubic feet, and then find the total remaining volume of water in the cylinder after the cube is submerged.

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