
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 \( G(4) = 35 \) and
\[
\frac{G(4x)}{G(x+2)} = 4 - \frac{20x+24}{x^2+4x+4}
\]
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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