
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
 $p,q,r$  are real numbers satisfying \[\frac{(p+q)(q+r)(r+p)}{pqr} = 24\] \[\frac{(p-2q)(q-2r)(r-2p)}{pqr} = 10.\] Given that  $\frac{p}{q} + \frac{q}{r} + \frac{r}{p}$  can be expressed in the form  $\frac{m}{n}$ , where  $m,n$  are relatively prime positive integers, compute  $m+n$ .

*Author: Alex Zhu*

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