
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
In a box, there are six balls marked with the numbers 1 through 6, which are of the same size. If two balls are drawn from the box one after another, their numbers are noted and then the balls are put back. A prize is won if the product of the two numbers is a multiple of 4. With four people participating in the drawing and each drawing twice, what is the probability that exactly three people win a prize?

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