
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 \( F(x) \) be a polynomial such that \( F(8) = 33 \) and
\[
\frac{F(4x)}{F(x+4)} = 16 - \frac{64x+64}{x^2+6x+8}
\]
for \( x \in \mathbb{R} \) where both sides are defined. Find \( F(16) \).

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