
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 $x$ be a solution of $x^{2}+x+1=0$. Then $x \neq 0$ and therefore we can divide both sides of the equation by $x$, obtaining $x+1+\frac{1}{x}=0$. From the equation, we have that $x+1=-x^{2}$, thus $-x^{2}+\frac{1}{x}=0$, that is: $x^{2}=1 / x$ or $x^{3}=1$ and $x=1$. Substituting $x=1$ into the equation $x^{2}+x+1=0$, we find $3=0$. Where did we go wrong?

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