
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
An octahedron consists of two square-based pyramids glued together along their square bases to form a polyhedron with eight faces. Imagine an ant that begins at one of the middle vertices of the octahedron, and walks to one of the four adjacent vertices that he randomly selects and calls vertex A. From vertex A, the ant then walks to one of the three other adjacent vertices that he randomly selects and calls vertex B. What is the probability that vertex B will be the opposite middle vertex directly across the original starting point? Express your answer as a common fraction.

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