
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 $F(4) = 22$ and \[\frac{F(2x)}{F(x+2)} = 4-\frac{16x+8}{x^2+x+1}\] for $x \in \mathbb{R}$ such that both sides are defined. Find $F(8)$.

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