
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
Say we have a cubic polynomial $81x^3 - 243x^2 + 216x - 64 = 0$, and you know that the roots are in geometric progression. Find the ratio of the largest to the smallest root.
A) $r^2$
B) $\frac{3}{2}$
C) $\frac{9}{8}$
D) $3r^2$

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