
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
Laura has a rectangular prism-shaped tank with dimensions $8$ inches, $10$ inches, and $12$ inches. She fills this tank to one third full with water. Then she places eight ice cubes, each measuring $2$ inches on each side, into the tank. How much of the tank is unoccupied by both water and ice?

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