
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
The roots of $81x^3 - 162x^2 + 108x - 18 = 0$ are in arithmetic progression. The difference between the largest and smallest roots is?
A) $\frac{2}{3}$  
B) $\frac{3}{4}$  
C) $\frac{1}{2}$  
D) $\frac{3}{8}$  
E) $\frac{1}{4}$

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