
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
Given that the graph of the function $y=g(x)$ has a horizontal asymptote at $\frac{1}{3}$ and vertical asymptotes at $x = -3$ and $x = 4$. The function is described by $g(x) = \frac{x^2 + Dx + E}{2x^2 - Fx - 18}$, where $D, E, F$ are integers. For all $x > 4$, it is true that $g(x) > 0.3$. Find $D + E + F$.

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