
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
The equation $\sqrt{x + 12} - \frac{8}{\sqrt{x + 12}} = 4$ needs to be solved for real values of $x$.
A) $4 + 8\sqrt{3}$  
B) $4 - 8\sqrt{3}$  
C) $4 \pm 8\sqrt{3}$  
D) No real solutions

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