
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
Each edge of a cube is colored either red, black, or blue. Every face of the cube must have edges of at least two different colors. What is the smallest number possible of edges that must be colored neither red nor white (i.e., must be blue or black)?
A) 3  
B) 4  
C) 5  
D) 6  
E) 7

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