
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
Let  $x_1,x_2, ..., x_n$  be non-negative real numbers. Solve the system of equations:  $$ x_k+x_{k+1}=x^2_{k+2}\,\,,\,\,\, (k =1,2,...,n), $$  where  $x_{n+1} = x_1$ ,  $x_{n+2} = x_2$ .

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