
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 quadratic equation in terms of $x$, $x^{2}-2(a-2)x-b^{2}+16=0$.

(1) If $a$ and $b$ are the points obtained by throwing a dice twice, find the probability that the equation has two positive roots.

(2) If $a∈(2, 6]$ and $b∈(0, 4]$, find the probability that the equation has no real roots.

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