
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
The graph of the function $g(x) = ax^4 + bx^3 + cx^2 + dx + e$ is given. The function intersects the x-axis at $x = -1, 0, 1, 2$ and passes through the point $(0,3)$. Determine the coefficient $b$.

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