
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 teacher distributes four types of stickers — star, heart, circle, and square — to four students. Each student should receive one sticker of each type. The teacher randomly assigns four stickers to each student from a total of 16 stickers, which are indistinguishable once packed. Calculate the probability that each student receives one sticker of each type, expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are coprime integers. Find $p+q$.

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