
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
Each of the 24 balls is tossed independently and at random into one of the 6 bins. Let $p$ be the probability that one bin ends up with 3 balls, two bins each with 4 balls, and the remaining three with 5 balls each. Let $q$ be the probability that each bin ends up with 4 balls. Calculate $\frac{p}{q}$.
A) $\frac{1}{24}$
B) $\frac{1}{12}$
C) $\frac{5}{24}$
D) $\frac{1}{6}$
E) $\frac{1}{4}$

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