
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 $y = g(x)$ where $g(x) = \frac{x^2}{Dx^2 + Ex + F}$, and $D, E, F$ are integers. The graph has vertical asymptotes at $x = -3$ and $x = 2$. It is also given that for all $x > 5$, $g(x) > 0.5$. If additionally, $g(0) = \frac{1}{4}$, find $D + E + F$.

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