
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
We have 1000 solid cubes with edge lengths of 1 unit each. We want to use these small cubes to create a hollow cube with a wall thickness of 1 unit. The small cubes can be glued together but not cut. What is the maximum (external) volume of the cube we can thus create?

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