
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]


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A rectangular tank measures 12 inches in length, 10 inches in width, and 8 inches in height. It is filled to one-third of its capacity with water. Then, twelve ice cubes, each measuring 1 inch on all sides, are added to the tank. Calculate the volume, in cubic inches, that remains unoccupied by either water or ice inside the tank.

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