
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 conference center prepared breakfast for each of four guests. The breakfast included four types of rolls—nut, cheese, fruit, and veggie rolls. The preparer wrapped each of the 16 rolls (four of each type) and mixed them so that they became indistinguishable from one another. The rolls were then randomly distributed with four rolls per guest. Calculate the probability that each guest received one of each type of roll. Express the result as a fraction $\frac{m}{n}$, where $m$ and $n$ are coprime integers, and find $m+n$.

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