
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 \( a, b, \) and \( c \) be the roots of the cubic polynomial \( 3x^3 - 9x^2 + 54x - 12 \). Compute 
\[
(a+2b-2)^3 + (b+2c-2)^3 + (c+2a-2)^3.
\]

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