
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
The numbers $1, 2, 3, 4, 5, 6, 7, 8, 9$ are randomly placed on the faces of a regular octahedron, with each face containing a unique number. The probability that no two consecutive numbers (where $9$ and $1$ are consecutive) are on faces sharing an edge, and no odd number is adjacent to an even number, is $m/n$, where $m$ and $n$ are coprime positive integers. Find $m+n$.

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