
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
Point P is a moving point on the line $kx+y+3=0$ ($k>0$), and PA, PB are two tangents to the circle $C: x^2-2x+y^2=0$ with A and B being the points of tangency. If the minimum area of quadrilateral PACB is 2, then the value of the real number $k$ is \_\_\_\_\_\_.

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