
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
Given 8 unit cubes, each of whose 48 square faces can be painted either black or white, devise a way to arrange these cubes into a larger 2x2x2 cube such that exactly half (24) of the larger cube's 48 faces are black. Determine all possible values of \( n \), the number of black faces on the original 8 unit cubes.

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