
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
Let $G(x)$ be a polynomial such that $G(4) = 8$ and
\[
\frac{G(4x)}{G(x+4)} = 16 - \frac{96x+192}{x^2+8x+16}
\]
for $x \in \mathbb{R}$ such that both sides are defined. Find $G(8)$.

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