
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
Jimmy owns a cube-shaped container that measures $12$ inches on each side. He fills this container with water until it is three-quarters full. Then he throws twelve ice cubes that measure $1.5$ inches on each side into the container. Assume that half of these ice cubes melt completely before settling. In inches cubed, how much of the container is unoccupied by ice or water?

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