
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 bug starts at one vertex of a tetrahedron and moves along the edges according to the following rule. At each vertex, the bug will choose to travel along one of the three edges emanating from that vertex. Each edge has equal probability of being chosen, and all choices are independent. What is the probability that after three moves the bug will have visited every vertex exactly once?
**A)** $\frac{1}{9}$
**B)** $\frac{2}{9}$
**C)** $\frac{1}{3}$
**D)** $\frac{4}{9}$

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