
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
Now, we have $20$ balls which are tossed independently and at random into one of the $6$ bins. Let $p$ be the probability that some bin ends up with $2$ balls, another with $5$ balls, and the other four bins containing $3$ balls each. Let $q$ be the probability that two bins end up with $5$ balls each and the remaining four bins contain $2$ balls each. Calculate $\frac{p}{q}$.
A) $\frac{1}{2}$
B) $1$
C) $2$
D) $4$
E) $5$

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