
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 \( p, q, \) and \( r \) be the roots of \( x^3 - 8x^2 + 10x - 3 = 0 \). Calculate
\[
\frac{p}{qr + 2} + \frac{q}{pr + 2} + \frac{r}{pq + 2}.
\]

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