
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
A cube with edge length $n$ units (where $n$ is an integer $>2$) is painted such that each face has a single color, either black or white, with adjacent faces being painted in alternate colors. After fully painting, the cube is sliced into $n^3$ smaller cubes of unit length. If the number of smaller cubes with exactly one face painted black equals the number of smaller cubes completely free of paint, find $n$.
A) 4
B) 5
C) 6
D) 7
E) None of the above

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