
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
Eight ants are placed on the eight vertices of a regular cube. Each ant independently moves simultaneously from its vertex to one of the three adjacent vertices with equal probability. What is the probability that no two ants end up on the same vertex after the move?
A) \( \frac{64}{729} \)
B) \( \frac{1}{729} \)
C) \( \frac{128}{6561} \)
D) \( \frac{1}{6561} \)
E) \( \frac{128}{729} \)

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