
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 the positive numbers $x$ and $y$ satisfy the equation $x^2 + 2xy - 1 = 0$, find the minimum value of $2x + y$. The options are:
A) $\frac{\sqrt{2}}{2}$
B) $\sqrt{2}$
C) $\frac{\sqrt{3}}{2}$
D) $\sqrt{3}$

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