
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 functions $f(x) = x^3 + ax^2 - 4x + c$ and $g(x) = \ln x + (b-1)x + 4$, the equation of the tangent line to the curve $y = f(x)$ at $x = 1$ is $3x - y + 1 = 0$.  
(I) Determine the expression for $f(x)$.  
(II) If for all $x_1 \in [-3, 0]$ and $x_2 \in [0, +\infty)$ it holds that $f(x_1) \ge g(x_2)$, find the range of values of $b$.

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