
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
Suppose you independently toss 15 balls at random into one of 5 bins. Let \( p \) be the probability that each bin ends up with exactly 3 balls, and let \( q \) be the probability that the bins end up with 5 balls, 4 balls, 2 balls, 2 balls, and 2 balls respectively. Calculate the value of \( \frac{p}{q} \).

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