
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 a circle $C: (x-1)^{2} + (y-1)^{2} = 16$ and a line $l: (2m-1)x + (m-1)y - 3m + 1 = 0$. When the chord intercepted by the line $l$ on the circle $C$ achieves the minimum length, the equation of the line $l$ is ______.

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