
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
Investigate the properties of the function $f(x)=\frac{\ln x}{x}$ and complete the following two questions:

1. Arrange $f(2)$, $f(3)$, and $f(5)$ in ascending order: $\_\_\_\_\_\_$
2. The maximum value of the function $g(x)=x^{\frac{1}{x}}(x>0)$ is: $\_\_\_\_\_\_$

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