
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 \( P \) is a moving point on the line \( l: kx + y + 4 = 0 \) (where \( k > 0 \)), and \( PA \) and \( PB \) are two tangents to the circle \( C: x^2 + y^2 - 2y = 0 \), with \( A \) and \( B \) being the points of tangency. If the minimum area of the quadrilateral \( PACB \) is 2, find the value of \( k \).

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