
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 cafeteria prepared snacks for each of four students. Each snack package should have consisted of three types of cookies: chocolate, vanilla, and strawberry. The cafeteria worker wrapped each of the twelve cookies and once wrapped, the cookies were indistinguishable from one another. She then randomly put three cookies in a package for each of the students. Given that the probability each student got one cookie of each type is $\frac{p}{q},$ where $p$ and $q$ are relatively prime integers, find $p+q.$

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