
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 equation of a circle is $x^{2}+y^{2}-2x+2y+m-3=0$ $(m \in \mathbb{R})$.  
$(1)$ Find the range of values of $m$;  
$(2)$ If $m=1$, find the length of the chord which the circle cuts from the line $x-y-4=0$.

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