
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 $a > 2$, then find the sum of the real solutions of the equation:
\[ \sqrt{a - \sqrt{a - x}} = x \]
A) $\frac{\sqrt{4a} - 1}{2}$
B) $\frac{\sqrt{4a-1} - 1}{2}$
C) $\frac{\sqrt{4a-2} - 1}{2}$
D) $\frac{\sqrt{4a-3} - 2}{2}$
E) $\frac{\sqrt{4a-3} - 1}{2}$

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