
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
Regarding the function $y=\log_{2}(x^{2}-2x+3)$, there are the following four conclusions:  
① The domain is $(-\infty, -3] \cup (1, +\infty)$;  
② The increasing interval is $[1, +\infty)$;  
③ The minimum value is 1;  
④ The graph is always above the x-axis.  
Among these, the correct conclusions are.

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