
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
Given the function $f(x)=x^{2}-2ax+{b}^{2}$, where $a$ and $b$ are real numbers.
(1) If $a$ is taken from the set $\{0,1,2,3\}$ and $b$ is taken from the set $\{0,1,2\}$, find the probability that the equation $f(x)=0$ has two distinct real roots.
(2) If $a$ is taken from the interval $[0,2]$ and $b$ is taken from the interval $[0,3]$, find the probability that the equation $f(x)=0$ has no real roots.

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