
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
Let $a$ and $b$ be positive numbers satisfying $a - 2ab + b = 0$. Find the minimum value of $2a + b$, with answer choices given below.

A) $\frac{3}{2} + \sqrt{2}$
B) $2\sqrt{2}$
C) $1 + \sqrt{2}$
D) $3$

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