
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
(1) Suppose there is a quadratic equation about $x$ ($x^{2} + x + b^{2} = 0$). If $b$ is a randomly chosen number from the interval $[0, 2]$, find the probability that this equation has real roots.

(2) There are 3 red balls, 5 white balls, and 2 black balls in a bag, all of the same size and quality. If 3 balls are randomly drawn from the bag, find the probability of events $A$ and $B$:
    (①) Event $A$: Exactly one red ball, one white ball, and one black ball.
    (②) Event $B$: At least one red ball.

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