
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 \(p\), \(q\), \(r\) be distinct real numbers such that
\[
\frac{p}{q-r} + \frac{q}{r-p} + \frac{r}{p-q} = 3.
\]
Find all possible values of 
\[
\frac{p^2}{(q-r)^2} + \frac{q^2}{(r-p)^2} + \frac{r^2}{(p-q)^2}.
\]

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