
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 cards are placed into a box, each bearing a number 1 through 5, with each number entered on ten cards. Four cards are drawn from the box at random and without replacement. Let \( p \) be the probability that all four cards bear a number belonging to the subset {1, 2, 3}. Let \( q \) be the probability that three of the cards bear a number from subset {1, 2, 3}, and the other bears a number from subset {4, 5}. What is the value of \( q/p \)?

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