
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 side of a cube has a stripe drawn diagonally from one vertex to the opposite vertex. The stripes can either go from the top-right to bottom-left or from top-left to bottom-right, chosen at random for each face. What is the probability that there is at least one continuous path following the stripes that goes from one vertex of the cube to the diagonally opposite vertex, passing through consecutively adjacent faces?
-  A) $\frac{1}{128}$
-  B) $\frac{1}{32}$
-  C) $\frac{3}{64}$
-  D) $\frac{1}{16}$
-  E) $\frac{1}{8}$

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