
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 packed breakfast for each of three guests. Each breakfast should have consisted of four types of rolls: one each of nut, cheese, fruit, and veggie rolls. The preparer wrapped each of the twelve rolls and once wrapped, the rolls were indistinguishable from one another. She then randomly put four rolls in a bag for each of the guests. Compute the probability each guest got one roll of each type and express this probability in the form $\frac mn,$ where $m$ and $n$ are relatively prime integers. Then find $m+n.$

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