
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
Given that each of the 25 balls is tossed independently and at random into one of the 4 bins, calculate the ratio of the probability that two bins end up with 6 balls each, and the other two bins with 5 balls each, to the probability that each bin ends up with 6 balls, and the remaining bin with 1 ball.

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