
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 function \( y = g(x) = \frac{x^2}{Ax^2 + Bx + C} \), where \( A, B, \) and \( C \) are integers. The function has vertical asymptotes at \( x = -1 \) and \( x = 2 \), and for all \( x > 4 \), it is true that \( g(x) > 0.5 \). Determine the value of \( A + B + C \).

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