
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:
\[
\frac{xz}{x + y} + \frac{yx}{y + z} + \frac{zy}{z + x} = 2
\]
and
\[
\frac{zy}{x + y} + \frac{xz}{y + z} + \frac{yx}{z + x} = 3.
\]
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