
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 height of 12 feet is completely filled with water. A solid cube with a side length of 10 feet is submerged into the cylinder such that one of its body diagonals remains vertical. Calculate the volume of water displaced by the cube.

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