
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
If $|x - y^2| = x + y^2$ where $x$ and $y$ are real numbers, then determine the values of $x$ and $y$ that satisfy the equation.
**A)** \(x = 0\) and \(y = 1\)  
**B)** \(x = 1\) and \(y = 0\)  
**C)** \(x = 0\) and \(y = 0\)  
**D)** \(x = 1\) and \(y = 1\)  
**E)** None of these

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