
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
\[
\frac{p}{(q - r)^2} + \frac{q}{(r - p)^2} + \frac{r}{(p - q)^2}.
\]

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