
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 $25$ balls is tossed independently and at random into one of the $5$ bins. Let $r$ be the probability that some bin ends up with $6$ balls, another bin ends up with $7$ balls, and the other three bins with $4$ balls each. Let $s$ be the probability that two bins each end up with $5$ balls and the other three with $5$ balls each as well. Calculate the value of $\frac{r}{s}$.

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