
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 of the system

\[ 1 - x_1^2 = x_2, \quad 1 - x_2^2 = x_3, \quad \ldots, \quad 1 - x_{n-1}^2 = x_n, \quad 1 - x_n^2 = x_1 \]

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