
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 the function $y=f(x)$ ($x \in \mathbb{R}$) whose graph passes through the point $(e, 0)$, where $f'(x)$ is the derivative of $f(x)$ and $e$ is the base of the natural logarithm. If for $x > 0$, $xf'(x) < 2$ always holds, then the solution set of the inequality $f(x) + 2 \geq 2\ln x$ is \_\_\_\_\_\_.

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