
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 terms of $x$: $x^2 - ax + \frac{1}{4}b^2 = 0$,

(1) If $a$ is chosen from the numbers $0$, $1$, $2$, and $b$ is chosen from the numbers $0$, $1$, $2$, $3$, calculate the probability that the above equation has real roots.

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

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