
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
Given that $x \in R$, $y > 0$, set $A = \{ x^2 + x + 1, -x, -x - 1 \}$, and set $B = \{ -y, -\frac{y}{2}, y + 1 \}$. If $A = B$, find the value of $x^2 + y^2$.

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