
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
Sarah has a cube-shaped tank that measures $12$ inches on every side. She fills the tank with water until it is one-third full. Later, Sarah adds fifteen small spherical marbles, each with a diameter of $1$ inch, into the tank. Calculate the volume, in cubic inches, of the space within the tank that is unoccupied by either water or marbles.

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