
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 a cubic polynomial $f(x) = ax^3 + bx^2 + cx + d$ is provided. You are to find out the value of $b$. The known points on the curve are $(-2,0)$, $(2,0)$, and $(0,3)$.

[asy]
unitsize(1.5 cm);

real func(real x) {
  return((x + 2)*(x - 2)*(x - 1));
}

draw(graph(func,-2.4,2.5));
draw((-2.5,0)--(2.5,0),Arrows(6));
draw((0,-1)--(0,3),Arrows(6));

label("$x$", (2.5,0), E);
label("$f(x)$", (0,3), N);

dot("$(-2,0)$", (-2,0), SW, fontsize(10));
dot("$(2,0)$", (2,0), SE, fontsize(10));
dot("$(0,3)$", (0,3), NE, fontsize(10));
[/asy]

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