
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 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 tangent lines that are vertical to the $y$-axis, find the range of $a$.

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