
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 wooden cube $n$ units on a side is painted red on just four vertical faces (leaving the top and bottom unpainted) and then cut into $n^3$ unit cubes. Exactly one-third of the total number of faces of the unit cubes are red. What is $n$?
A) 2  
B) 4  
C) 5  
D) 6  
E) 8

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