
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 $P(x,y)$ is a point on the line $kx+y+4=0 (k > 0)$, and $PA$ is a tangent line of circle $C$: $x^{2}+y^{2}-2y=0$, with $A$ being the point of tangency. If the minimum length of $PA$ is $2$, find the value of $k$.

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