
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
There are 2 red balls, 2 white balls, and 2 black balls in a bag, making a total of 6 balls. In a game, 3 balls are randomly drawn from the bag. If one ball of each color is drawn, the player wins; otherwise, they lose. What is the probability of winning? Furthermore, if 3 people participate in this game, what is the probability that exactly 1 person wins?

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