
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
Given real numbers \( x, y, z \) satisfying
\[
\frac{y}{x-y}=\frac{x}{y+z}, \quad z^{2}=x(y+z)-y(x-y)
\]
find the value of
\[
\frac{y^{2}+z^{2}-x^{2}}{2 y z}.
\]

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