
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
Suppose each face of a cube either has a narrow stripe from the center of one edge to the center of the opposite edge or a dot at the center. Each face's design (stripe or dot) is chosen randomly and independently with equal probability. What is the probability that there is a continuous stripe encircling the cube without interruption by dots?
A) $\frac{768}{59049}$
B) $\frac{2}{81}$
C) $\frac{4}{243}$
D) $\frac{8}{729}$
E) $\frac{16}{2187}$

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