
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 $x,$ $y,$ $z,$ $w$ be real numbers such that
\[\frac{(x - y)(z - w)}{(y - z)(w - x)} = \frac{1}{3}.\]Find the sum of all possible values of
\[\frac{(x - z)(y - w)}{(x - y)(z - w)}.\]

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