
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 $f(x)= \frac {2}{x}+\ln x$, consider the following four propositions:  
$① x=2$ is a local minimum point of $f(x)$;  
$②$ The function $f(x)$ has a unique zero point in $(0,+\infty)$;  
$③$ There exists a positive real number $k$, such that $f(x) > kx$ always holds;  
$④$ For any two positive real numbers $x_{1}$, $x_{2}$, and $x_{1} < x_{2}$, if $f(x_{1})=f(x_{2})$, then $x_{1}+x_{2} > 4$.  
Among these, the true propositions are \_\_\_\_\_\_ .

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