
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 $y=\log_{4}(x^{2}-2x+5)$, there are the following four conclusions: Among them, the correct ones are ① The domain is $\mathbb{R}$; ② The increasing interval is $[1, +\infty)$; ③ The minimum value is 1; ④ The graph is always below the x-axis.

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