
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 hotel prepares breakfast bags for each of three guests. Each breakfast should include four types of rolls: nut, cheese, fruit, and vegetable rolls. The preparer wraps each of the twelve rolls. Once wrapped, the rolls become indistinguishable from one another. She randomly puts four rolls in a bag for each guest. Determine the probability that each guest receives one roll of each type, expressed as a fraction $\frac{m}{n}$ where $m$ and $n$ are relatively prime integers. Find $m+n.$

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