
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

$$
\left\{
\begin{array}{l}
2 \sin x = \tan y \\
2 \cos y = \cot z \\
\sin z = \tan x
\end{array}
\right.
$$

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

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