
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 an integer  $n \ge 2$ , solve in real numbers the system of equations \begin{align*}
\max\{1, x_1\} &= x_2 
\max\{2, x_2\} &= 2x_3 
&\cdots 
\max\{n, x_n\} &= nx_1.  
\end{align*}

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