
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
Given two quadratic equations where $x^2 + ax + b = 0$ has roots $r$ and $s$. If $r^2$ and $s^2$ are the roots of another quadratic equation $x^2 + cx + d = 0$, find an expression for $c$ and $d$ in terms of $a$ and $b$, given that $rs = 2b$.

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