
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 &= \sin(a+b+c), \\
y &= \sin(b+c+d), \\
z &= \sin(c+d+a), \\
w &= \sin(d+a+b),
\end{align*}
where \(a,b,c,d\) are angles measured in degrees.

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