
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
In a geometric sequence where all terms are positive, ${a_3}$ and ${a_{15}}$ are the roots of the equation ${x^2 - 6x + 8 = 0}$. Determine the value of $\frac{{a_1a_{17}}}{{a_{9}}}$.

A) $2\sqrt{2}$
B) $4$
C) $\pm 2\sqrt{2}$
D) $\pm 4$

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