
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 face of a cube is painted with a single narrow stripe from the center of one edge to the center of the opposite edge. Each stripe can be chosen to be either red or blue, and the orientation of the stripe (which edges it connects) is chosen at random and independently for each choice. What is the probability that there is a continuous stripe of either color encircling the cube?
A) $\frac{3}{512}$
B) $\frac{1}{512}$
C) $\frac{1}{256}$
D) $\frac{1}{1024}$
E) $\frac{3}{1024}$

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