
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 $b > 2$, find the sum of the real solutions to the equation
\[
\sqrt{b - \sqrt{b + y}} = y.
\]
A) $\sqrt{b} - 1$
B) $\dfrac{\sqrt{b}- 1}{2}$
C) $\sqrt{b - 1}$
D) $\dfrac{\sqrt{b - 1}}{2}$
E) $\dfrac{\sqrt{4b- 3} - 1}{2}$

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