
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 point A(0, 5) and the circle C with the equation $x^2+y^2+4x-12y+24=0$.

1. If a line $l$ passes through A(0, 5) and the chord it cuts from circle C has a length of $4\sqrt{3}$, find the equation of the line $l$.
2. Given the points M(-1, 0), N(0, 1), and a variable point Q on circle C, find the minimum area of triangle $\triangle QMN$.

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