
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
Consider the quadratic equation in $x$: $x^2 + 2ax + b^2 = 0$.

(1) If $a$ is chosen from the set $\{0, 1, 2, 3\}$ and $b$ is chosen from the set $\{0, 1, 2, 3\}$, find the probability that the given equation has real roots.

(2) If $a$ is chosen from the interval $[0, 3]$ and $b$ is chosen from the interval $[0, 2]$, find the probability that the given equation has real roots.

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