
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
Consider the graph of the equation \( y = \frac{x}{x^3 + Ax^2 + Bx + C} \), where \( A, B, C \) are integers. The graph shows that there are vertical asymptotes at \( x = -3, 1, 3 \). Identify \( A, B, \) and \( C \) and compute \( A + B + C \).

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