
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 packs breakfast for each of four guests. Each breakfast should consist of two types of rolls, one cheese roll and one fruit roll. The preparer wrapped each of the eight rolls, four cheese and four fruit. Once wrapped, the rolls were indistinguishable from one another. She then randomly put two rolls in a bag for each of the guests. Calculate the probability that each guest got one roll of each type, expressed as $\frac{m}{n}$ where $m$ and $n$ are relatively prime integers, and find the sum $m+n$.

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