
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 &= z + w + zw - zwx, \\ 
y &= w + x + wx - wxy, \\
z &= x + y + xy - xyz, \\
w &= y + z + yz - yzw.
\end{align*}

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