
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
Compute the number of real solutions \((x, y, z, w)\) to the system of equations:
\[
\begin{array}{rlrl}
x & = z + w + z w x \\
z & = x + y + x y z \\
y & = w + x + w x y \\
w & = y + z + y z w
\end{array}
\]

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