
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
Among the following propositions, the correct ones are __________. (Fill in the serial numbers of all correct propositions)  
① The graph of the function $y=\log_{2}(x-3)+2$ can be obtained by translating the graph of $y=\log_{2}x$ upwards by 2 units and to the right by 3 units;  
② The graph of the function $f(x)= \frac {2x-3}{x+1}$ is centrally symmetric about the point (1, 2);  
③ In the interval $(0, +\infty)$, the graph of the function $y=x^{ \frac {1}{2}}$ is always above the graph of the function $y=x$;  
④ It is impossible for the graph of any function to intersect a line perpendicular to the x-axis at two points.

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