
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 guesthouse prepared breakfast packs for each of three guests, including four types of rolls: nut, cheese, fruit, and chocolate. Each guest was meant to receive one of each type, making a total of 12 rolls prepared. After wrapping, the rolls were indistinguishable from one another. The rolls were then placed randomly in bags, three rolls per guest. Calculate the probability that each guest received exactly one roll of each type, expressed in the form $\frac{m}{n}$ where $m$ and $n$ are relatively prime integers.

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