
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 $30$ balls are tossed independently and at random into one of the $6$ bins. Let $p$ be the probability that one bin ends up with $3$ balls, another with $6$ balls, another with $5$, another with $4$, another with $2$, and the last one with $10$ balls. Let $q$ be the probability that each bin ends up with $5$ balls. Calculate $\frac{p}{q}$.
A) 0.5
B) 0.125
C) 0.025
D) 0.0125

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