
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
Part of the graph of the polynomial function $g(x) = ax^3 + bx^2 + cx + d$ is given. The roots of $g(x)$ include $-2$ and $1$, and the function passes through the point $(0, 3)$. Additionally, the derivative $g'(1) = 0$. Determine the value of $b$.

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