
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 an opaque box, there are three white balls and two black balls with distinct identifiers. The white balls are labeled $a_1$, $a_2$, $a_3$, and the black balls are labeled $b_1$, $b_2$. Two balls are drawn at random from the box.
(1) List all the possible different outcomes;
(2) Calculate the probability of drawing exactly one white ball and one black ball;
(3) Calculate the probability of drawing at least one white ball.

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