
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
Given that $a$ and $b$ are positive real numbers satisfying $\frac{2}{a} + \frac{1}{b} = 1$, let $x = a + b$. Find the range of the real number $x$.

A) $[6, +\infty)$
B) $[2\sqrt{2}, +\infty)$
C) $[4\sqrt{2}, +\infty)$
D) $[3+2\sqrt{2}, +\infty)$

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