
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 \( r_{1}, r_{2}, r_{3}, r_{4} \) be the four roots of the polynomial \( x^{4}-4 x^{3}+8 x^{2}-7 x+3 \). Find the value of
\[
\frac{r_{1}^{2}}{r_{2}^{2}+r_{3}^{2}+r_{4}^{2}}+\frac{r_{2}^{2}}{r_{1}^{2}+r_{3}^{2}+r_{4}^{2}}+\frac{r_{3}^{2}}{r_{1}^{2}+r_{2}^{2}+r_{4}^{2}}+\frac{r_{4}^{2}}{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}
\]

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