
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
A pocket contains 5 balls of the same size, among which are 3 white balls and 2 black balls. Two balls are drawn from the pocket at once.

1. How many basic events are there in total, and list them out.
2. What is the probability that both balls drawn are white.
3. What is the probability that one ball drawn is black, and the other is white.

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