
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
Fifty slips are placed into a hat, each bearing a number from 1 to 10. Numbers 1 to 5 are each entered on five slips, and numbers 6 to 10 are each entered on three slips. Four slips are drawn at random without replacement. Let $r$ be the probability that all four slips bear the same number, which only happens for numbers 1 to 5. Let $s$ be the probability that two of the slips bear a number $c$ (among the numbers 1 to 5) and the other two slips bear a number $d\ne c$ (among numbers 6 to 10). What is the value of $s/r$?

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