
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 room packed breakfast for each of four guests. Each breakfast should consist of four types of rolls: nut, cheese, fruit, and veggie rolls. The preparer wrapped each of the 16 rolls, and once wrapped, the rolls were indistinguishable from one another. She then randomly distributed four rolls in a bag for each of the guests. Given that the probability each guest got one roll of each type is $\frac mn,$ where $m$ and $n$ are relatively prime integers, find $m+n.$

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