
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
Given an opaque box containing $6$ balls, of which $3$ are red, $2$ are white, and $1$ is black. The balls are identical in all aspects except for color. If $3$ balls are randomly drawn from the box, calculate the probability of the following events:
1. Exactly one red ball and one white ball;
2. At least two red balls;
3. No black balls.

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