
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
Find all real solutions  $(x,y,z)$  of the system of equations:
\[
\begin{cases}
 \tan ^2x+2\cot^22y=1  
 \tan^2y+2\cot^22z=1  
  \tan^2z+2\cot^22x=1  
\end{cases}
\]

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