
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  $x^3 + a x^2 + b x + c = 0$  are  $\alpha, \beta$  and  $\gamma.$  Find the cubic whose roots are  $\alpha^3, \beta^3, \gamma^3.$ 

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