
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 a line $l$: $x-my+3=0$ and a circle $C$: $x^{2}+y^{2}-6x+5=0$  
$(1)$ When the line $l$ is tangent to the circle $C$, find the value of the real number $m$;  
$(2)$ When the line $l$ intersects the circle $C$, and the chord length is $\dfrac{2\sqrt{10}}{5}$, find the value of the real number $m$.

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