
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 the equation $x^3 - 6x^2 + 11x - 6 = 0$ have three real roots $a$, $b$, and $c$. Find $\frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3}$.

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