
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 point $P(x,y)$ on the line $kx+y+4=0$ $(k > 0)$, and $PA,PB$ are two tangents from $P$ to the circle $C:x^2+y^2-2y=0$ (with $C$ as the center), determine the value of $k$ if the minimum area of the quadrilateral $PACB$ is $2$.

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