
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 depicted. For all \( x > 3 \), \( g(x) > 0.5 \). If \( g(x) = \frac{x^2}{Ax^2 + Bx + C} \), where \( A, B, \) and \( C \) are integers, determine \( A+B+C \).

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