
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 one-variable quadratic equation in $x$: $x^{2}-3x+m-3=0$.  
$(1)$ If this equation has two distinct real roots $x_{1}$ and $x_{2}$, find the range of values for $m$;  
$(2)$ If the roots of this equation are reciprocals of each other, find the value of ${x}_{1}^{2}+{x}_{2}^{2}$.

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