
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 circle $C:(x-2)^{2}+y^{2}=1$.

$(1)$ Find the equation of the tangent line that passes through point $P(3,m)$ and is tangent to circle $C$.

$(2)$ If point $Q$ is a moving point on the line $x+y-6=0$, and tangent lines $QA$ and $QB$ are drawn from $Q$ to circle $C$, where $A$ and $B$ are the points of tangency, find the minimum value of the area of quadrilateral $QACB$ and the coordinates of point $Q$ at this time.

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