
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 tank with radius $5$ feet and height $15$ feet is completely filled with water. A solid cube with side length $10$ feet is placed into the tank so that the diagonal of the cube is vertical. Calculate the square of the volume $v$ of water displaced in cubic feet.

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