
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 a quadratic equation in $x$, $a^2x^2+b^2x+c^2=0$, and another quadratic equation $ax^2+bx+c=0$, find the relationship between the coefficients $a$, $b$, and $c$.

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