
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{align*}
x &= w + z - wzw, \\ 
y &= w - x + wxy, \\
z &= x - y - xyz, \\
w &= y - z + yzw.
\end{align*}

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