
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 numbered 1, 2, 3, 4, 5, and 6, each of the same size. When two balls are drawn from the box at once, their numbers are recorded and then the balls are replaced. If the product of the two numbers is a multiple of 4, a prize is won. With four participants in the draw, find the probability that exactly three people win a prize.

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