
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 \( p, q, r, s \) be real numbers such that
\[
\frac{(p - q)(r - s)}{(q - r)(s - p)} = -\frac{3}{7}.
\]
Find the sum of all possible values of
\[
\frac{(p - r)(q - s)}{(p - q)(r - s)}.
\]

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