
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
Solve the equation $x^2 + x + 1 = \frac{1}{x^2 - x + 1}$, under the condition that $x^2 - x + 1 \neq 0$.
A) $x = 1$
B) $x = -1$
C) $x = \pm \sqrt{2}$
D) $x = 0$

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