
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 $|2x - \sqrt{z}| = 2x + \sqrt{z}$ where $x$ and $\sqrt{z}$ are real numbers, determine the values of $x$ and $z$.
A) $x \geq 0 \text{ and } z = 0$  
B) $x \geq 0 \text{ and } z = 1$  
C) $x \geq 1 \text{ and } z = 0$  
D) $x = 0 \text{ and } z = 0$  
E) $x = 1 \text{ and } z = 1$

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