
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
Suppose $a$ and $b$ are the points obtained by throwing a dice in order, and the function is $f(x)=\frac{1}{2}ax^{2}+bx+1$.

(1) Find the probability that $f(x)$ is a decreasing function in the interval $(-\infty,-1]$;

(2) Find the probability that the function $f(x)$ has zero points.

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