
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 $|2x - \log z| = 2x + \log z$ where $2x$ and $\log z$ are real numbers, determine $x$ and $z$.
**A)** $x = 0$  
**B)** $z = 1$  
**C)** $x = 0 \text{ and } z = 1$  
**D)** $x(z-1) = 0$  
**E)** None of these

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