
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
22. Given the function $f(x) = \frac{\ln x}{x}$.

(1) Find the extreme points of the function $f(x)$.

(2) Let $g(x) = xf(x) - ax^2 + \frac{\ln 2}{2} (a > 0)$. If the maximum value of $g(x)$ is greater than $\frac{a}{2} - 1$, find the range of $a$.

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