
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 that point $P(x, y)$ is a moving point on the line $kx + y + 4 = 0$ ($k > 0$), and $PA$, $PB$ are two tangents to the circle $C: x^2 + y^2 - 2y = 0$ with $A$, $B$ as the tangent points. If the minimum area of quadrilateral $PACB$ is 2, then the value of $k$ is $\boxed{2}$.

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