
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 equation of circle $C$ as $x^{2} - 2x + y^{2} = 0$ and line $l: kx - y + 2 - 2k = 0$, where it intersects with circle $C$ at points $A$ and $B$, find the slope of line $l$ when the area of triangle $\Delta ABC$ is at its maximum.

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