
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 given. For all \( x > 5 \), it is true that \( g(x) > 0.3 \). If \( g(x) = \frac{x^2}{Dx^2 + Ex + F} \), where \( D, E, \) and \( F \) are integers, determine \( D + E + F \). The function has vertical asymptotes at \( x = -3 \) and a horizontal asymptote at \( y = \frac{1}{D} \), with \( \frac{1}{D} < 1 \), and \( D \) being an integer.

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