
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
Suppose that the roots of the quadratic  $x^2 + ax + b$  are  $\alpha$  and  $\beta$ . Then  $\alpha^3$  and   $\beta^3$  are the roots of some quadratic  $x^2 + cx + d$ . Find  $c$  in terms of  $a$  and  $b$ .


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