
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 circle \( C: (x-1)^2 + (y-2)^2 = 25 \) and the line \( l: (2m+1)x + (m+1)y - 7m - 4 = 0 \) intersect, find the equation of line \( l \) when the chord length intercepted by the circle \( C \) is minimized.

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