
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
In the same octahedron setup, imagine now the ant starts at one of the middle ring vertices, which we will call vertex M. This vertex M is adjacent to four vertices: the top vertex, the bottom vertex, and two other middle ring vertices. If the ant moves randomly to one of these adjacent vertices, what is the probability that he lands either back at the starting vertex M or at the bottom vertex?

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