
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
\[\frac{xz}{x + y} + \frac{yz}{y + z} + \frac{xy}{z + x} = -10\]and
\[\frac{yz}{x + y} + \frac{zx}{y + z} + \frac{xy}{z + x} = 15.\]Compute the value of
\[\frac{y}{x + y} + \frac{z}{y + z} + \frac{x}{z + x}.\]

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