
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 \( x_1 \) and \( x_2 \) be the roots of the quadratic equation

\[ a x^2 + b x + c = 0. \]

Determine the equation whose roots are:
a) \( \frac{1}{x_1^3} \) and \( \frac{1}{x_2^3} \),
b) \( (x_1 - x_2)^2 \) and \( (x_1 + x_2)^2 \).

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