
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 solid cube has its faces randomly painted either red or blue, with each face independently deciding its color. What is the probability that the cube has at least one blue face on two opposite sides and at least one red face on two other opposite sides?
A) $\frac{27}{64}$
B) $\frac{32}{64}$
C) $\frac{54}{64}$
D) $\frac{24}{64}$

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