
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 circle $C: (x-1)^{2} + (y+1)^{2} = 4$.  
$(1)$ A tangent line $l$ is drawn from point $P(3,2)$ to circle $C$. Find the equation of the tangent line $l$.  
$(2)$ Let $Q$ be a moving point on the line $m: 3x-4y+8=0$. A tangent line is drawn from $Q$ to circle $C$ with the point of tangency being $M$. Find the minimum value of $|QM|$.

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