
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
Nine numbers, $1, 2, 3, 4, 5, 6, 7, 8,$ and $9$, are randomly chosen with one number left out and then assigned randomly to the faces of a regular cube so that each face contains a different number. Find the probability that no two consecutive numbers, where $9$ and $1$ are considered to be consecutive, are written on faces that share an edge. Express your answer as a fraction $m/n,$ where $m$ and $n$ are relatively prime positive integers, and find $m+n$.

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