
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
Given is a natural number  $n \geq 3$ . Solve the system of equations: $\[
\begin{cases}
\tan (x_1) + 3 \cot (x_1) &= 2 \tan (x_2) 
\tan (x_2) + 3 \cot (x_2) &= 2 \tan (x_3) 
& \dots 
\tan (x_n) + 3 \cot (x_n) &= 2 \tan (x_1) 
\end{cases}
\]$ 

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