
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
Since \(\left|a+\frac{1}{a}\right| \geqslant 2\) and equality is achieved only when \(|a|=1\), the first equation of the system is equivalent to \(\operatorname{tg} x= \pm 1, \sin y=1\). Then from the second equation, \(\cos z=0\).

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