
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 bakery prepared an assortment of 12 cookies for four children. Each cookie assortment should consist of three types of cookies: chocolate, vanilla, and strawberry, with four cookies of each type. The baker mixed all the cookies, and they became indistinguishable from one another. She then randomly divided the cookies among the four children, giving each child three cookies. Calculate the probability that each child received one cookie of each type, expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are relatively prime integers. Find $p+q.$

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