
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]


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In the cartesian coordinate plane $(xOy)$, the equation of circle $C$ is given by: $x^2 + y^2 - 8x + 11 = 0$, and the equation of line $l$ is given by: $(2m + 1)x + (m + 1)y - 7m - 4 = 0$.

(1) When $m = 1$, find the length of the chord cut by line $l$ on circle $C$.
(2) When line $l$ cuts the shortest chord on circle $C$, find the equation of line $l$.

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