
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 $f(x)=x^{3}+(1-a)x^{2}-a(a+2)x+b$ $(a,b\in\mathbb{R})$.
$(1)$ If the graph of the function $f(x)$ passes through the origin and the slope of the tangent line at the origin is $-3$, find the values of $a$ and $b$;
$(2)$ If the curve $y=f(x)$ has two tangents perpendicular to the $y$-axis, find the range of values for $a$.

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