
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 summer camp prepared a unique breakfast for each of four guests. Each breakfast was to contain four types of rolls: one each of nut, cheese, fruit, and chocolate rolls. Each type of roll was prepared three times, getting a total of twelve rolls. The rolls, once wrapped, looked identical from the outside. They were randomly distributed, with each guest receiving four rolls. Calculate the probability that each guest received one roll of each type. Represent this probability in the form $\frac{m}{n}$, where $m$ and $n$ are coprime integers and provide $m+n$.

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