
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 prepared breakfast packs for each of four guests. Each breakfast was to consist of four types of rolls – one each of nut, cheese, fruit, and veggie rolls. The rolls were wrapped such that they became indistinguishable from one another. The staff randomly distributed four rolls into each bag for the guests. Calculate the probability that each guest received one roll of each type. Let this probability be represented as $\frac{p}{q}$ where $p$ and $q$ are coprime integers. Find $p+q.$

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