
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 $y=g(x)$ is given. For all $x > 5$, it holds that $g(x) > 0.5$. The function $g(x)$ is defined as $g(x) = \frac{x^2}{Ax^2 + Bx + C}$ where $A$, $B$, and $C$ are integers. The vertical asymptotes of $g$ are at $x = -3$ and $x = 4$, and the horizontal asymptote is such that $y = 1/A < 1$. Find $A + B + C$.

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