
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 $G(8) = 20$ and 
\[
\frac{G(2x)}{G(x+2)} = 16 - \frac{80x + 84}{x^2 + 6x + 8}
\]
for $x \in \mathbb{R}$ such that both sides are defined. Find $G(16)$.

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