
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
There are 25 balls, each being tossed independently and randomly into one of 6 bins. Let $p$ represent the probability that one bin ends up with 5 balls, two bins with 4 balls each, and the other three with 3 balls each. Let $q$ represent the probability that each bin ends up with exactly 4 balls and one bin ends up with 5 balls. Calculate the ratio $\frac{p}{q}$.
A) $\frac{3}{5}$
B) 1
C) $\frac{5}{3}$
D) 2
E) 3

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