
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

Solve the system of equations:

\[
\begin{cases}
x + y = \frac{5xy}{1 + xy} \\
y + z = \frac{6yz}{1 + yz} \\
z + x = \frac{7zx}{1 + zx}
\end{cases}
\]

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