
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
Suppose $x,$ $y,$ and $z$ are real numbers such that
\[
\frac{xz}{x + y} + \frac{yx}{y + z} + \frac{zy}{z + x} = -5
\]
and
\[
\frac{yz}{x + y} + \frac{zx}{y + z} + \frac{xy}{z + x} = 7.
\]
Compute the value of
\[
x + y + z.
\]

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