
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 build a $4 \times 4 \times 4$ cube out of sugar cubes. How many different rectangular parallelepipeds can the sugar cubes determine, if the rectangular parallelepipeds differ in at least one sugar cube?

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