
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
For all triples \((x, y, z)\) satisfying the system

$$
\left\{\begin{array}{l}
\sqrt{3} \cos x=\operatorname{ctg} y \\
2 \cos y=\operatorname{tg} z \\
\cos z=2 \operatorname{ctg} x
\end{array}\right.
$$

find the minimum value of the expression \(\sin x+\sin z\).

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