
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
Sixty cards are placed in a box, each bearing a number from 1 through 15, with each number appearing on four cards. Four cards are drawn from the box at random without replacement. Let $p'$ be the probability that all four cards bear the same number. Let $q'$ be the probability that three of the cards bear a number $a$ and the fourth bears a number $b$, with $b \neq a$. What is the value of $\frac{q'}{p'}$?

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