
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 the line $l$ as $x-y+2=0$.  
$(1)$ Find the equation of the line parallel to line $l$ passing through point $A(3,-1)$.  
$(2)$ Find the length of the chord $MN$ intercepted by line $l$ on the circle $x^{2}+y^{2}-4x+4y-12=0$.

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