
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
Lily owns a cube-shaped container that measures $12$ inches on each side. She fills this container with water until it's one-third full. Then, she throws in twenty ice cubes, each measuring $1.5$ inches on each side. Assuming that all the ice cubes are submerged in the water, calculate in inches cubed how much of the container is unoccupied by water or ice after considering the ice's displacement of water.

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