
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: Quadratic function $y=x^{2}-4x+3$.  
$(1)$ Express $y=x^{2}-4x+3$ in the form of $y=a\left(x-h\right)^{2}+k$;  
$(2)$ Find the axis of symmetry, vertex coordinates, and maximum or minimum value of the graph of this quadratic function;  
$(3)$ For what values of $x$ does $y$ decrease as $x$ increases, when $-1\leqslant x \lt 3$? Find the range of $y$ in this interval.

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