
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 has each face divided diagonally into two triangles using a narrow stripe. Each triangle is painted either red or blue, chosen at random and independently. What is the probability that there is at least one face with both triangles the same color?
A) $\frac{31}{64}$
B) $\frac{1}{64}$
C) $\frac{63}{64}$
D) $\frac{1}{2}$
E) $\frac{1}{4}$

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