
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
Determine the ratio between the largest and the smallest roots of the polynomial $27x^3 - 54x^2 + 36x - 8 = 0$, given that the roots are in geometric progression.
A) $\frac{1}{2}$
B) $\frac{3}{2}$
C) $2$
D) $1$
E) $\frac{4}{3}$

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