
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 $x_1$, $x_2$ with $x_1 < x_2$, if $f(x_1) = f(x_2)$, then $x_1 + x_2 > 4$.  
Among these propositions, the true ones are \_\_\_\_\_\_.

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