
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
Two cubic equations. Let \( a, b, c \) be the roots of the equation \( x^3 + qx + r = 0 \). Write the equation whose roots will be the numbers

\[ \frac{b+c}{a^2}, \quad \frac{c+a}{b^2}, \quad \frac{a+b}{c^2} \]

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