
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 \((u,v,s,t)\) to the system of equations:
\begin{align*}
u &= s+t+sut, \\ 
v &= t+u+tuv, \\
s &= u+v+uvs, \\
t &= v+s+vst.
\end{align*}

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