
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
Solve the system of equations 
\[
\left\{
\begin{array}{l}
\sin x \cos y = \sin z \\
\cos x \sin y = \cos z
\end{array}
\right.
\]
if the numbers \( x \), \( y \), and \( z \) lie in the interval \(\left[0, \frac{\pi}{2}\right]\).

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