
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 cuboid with dimensions corresponding to length twice the cube's edge is painted with stripes running from the center of one edge to the center of the opposite edge, on each of its six faces. Each face's stripe orientation (either horizontal-center or vertical-center) is chosen at random. What is the probability that there is at least one continuous stripe that encircles the cuboid horizontally?
A) $\frac{1}{64}$
B) $\frac{1}{32}$
C) $\frac{1}{16}$
D) $\frac{1}{8}$
E) $\frac{1}{4}$

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