
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 four types of rolls: nut, cheese, fruit, and veggie rolls. The preparer wrapped each of the sixteen rolls (four of each type), and once wrapped, the rolls were indistinguishable from one another. She then randomly put four rolls in a bag for each of the guests. Calculate the probability that each guest got one roll of each type, given that at least two of the guests received no more than one type of roll twice.

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