
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
Let $P(x,y)$ be a moving point on the line $kx+y+4=0$ ($k > 0$), and $PA$ and $PB$ the two tangents to the circle $C: x^2 + y^2 - 2y = 0$ with the points of tangency at $A$ and $B$ respectively. Find the value of $k$ when the minimum area of the quadrilateral $PACB$ is $2$.

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