
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 numbers  $x_1, \dots, x_{2016}$  that satisfy the following equation for each  $1 \le i \le 2016$ . (Here  $x_{2017} = x_1$ .)
\[ x_i^2 + x_i - 1 = x_{i+1} \]

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