
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 function $y=g(x)$ is known to satisfy $g(x) > 0.3$ for all $x > 2$. The function $g(x)$ has the form $\frac{x^2}{Ax^2 + Bx + C}$, where $A, B, C$ are integers. Find $A+B+C$. Additional graphical information suggests that the vertical asymptotes are at $x = 1$ and $x = -3$.

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