
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 the line $l$: $(2k+1)x+(k-1)y-(4k-1)=0 (k\in R)$ and the circle $C$: $x^{2}+y^{2}-4x-2y+1=0$ intersect at points $A$ and $B$.
(1) Find the equation of line $l$ when $|AB|$ is minimum, and find the value of $|AB|$ in this case.
(2) Find the equation of the tangent line(s) to circle $C$ passing through point $P(4,4)$.

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