
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 function $y=g(x)$, characterized by the function $g(x) = \frac{x^2}{Px^2 + Qx + R}$, where $P$, $Q$, and $R$ are integers. For $x > 5$, it is true that $g(x) > 0.5$. From the graph, it is observed that there are vertical asymptotes at $x = -3$ and $x = 4$, and the horizontal asymptote occurs at a line $y = 1/P$. Determine the value of $P+Q+R$.

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