
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
(1) Given straight line $l_1: y=2x$ and straight line $l_2: x+y=3$ intersect at point $P$, when straight line $l$ passes through point $P$ and the distance from the origin $O$ to line $l$ is 1, find the equation of line $l$.  
(2) Given the circle $C: x^2+y^2+4x-8y+19=0$, draw the tangent line of circle $C$ passing through point $P(-4, 5)$, and find the equation of the tangent line.

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