
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
Let $a, b \in \mathbb{R}$, and the function $f(x)= \frac{1}{3}x^3 + ax^2 + bx + 1$, and $g(x)=e^x$ (where $e$ is the base of the natural logarithm), and the graph of $f(x)$ has a common tangent line with the graph of $g(x)$ at $x=0$.
(Ⅰ) Find the value of $b$;
(Ⅱ) Discuss the monotonicity of the function $f(x)$;
(Ⅲ) If $g(x) > f(x)$ holds for the interval $(-\infty, 0)$, find the range of values for $a$.

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