
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
Suppose \( p, \) \( q, \) and \( r \) are real numbers such that
\[
\frac{pr}{p + q} + \frac{qp}{q + r} + \frac{rq}{r + p} = -8
\]
and
\[
\frac{qr}{p + q} + \frac{rp}{q + r} + \frac{pq}{r + p} = 9.
\]
Compute the value of
\[
\frac{q}{p + q} + \frac{r}{q + r} + \frac{p}{r + p}.
\]

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