
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 6 bins. Let $r$ be the probability that two bins end up with 3 balls each, and the other four with 5 balls each. Let $s$ be the probability that two bins end up with 4 balls each, another two with 5 balls each, and the remaining two with 3 balls each. Calculate the value of $\frac{r}{s}$.

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