
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 three real numbers \(p, q,\) and \(r\) such that

\[ p+q+r=5 \quad \text{and} \quad \frac{1}{p+q}+\frac{1}{q+r}+\frac{1}{p+r}=9 \]

What is the value of the expression

\[ \frac{r}{p+q}+\frac{p}{q+r}+\frac{q}{p+r} ? \]

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