
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 equation \(y = \frac{x}{x^3 + Ax^2 + Bx + C}\), where \(A, B, C\) are integers, is given. The graph shows vertical asymptotes at \(x = -3, 0, 2\). Find the sum \(A + B + C\).

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