
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: $x^2+y^2-4x+2y-3=0$ and a point M(4, -8) outside the circle.  
(1) Draw tangents from M to circle C, touching the circle at points D and E, with the center of the circle at C. Find the length of the tangent and the equation of the line DE.  
(2) Draw a secant from M intersecting the circle at points A and B. If $|AB|=4$, find the equation of line AB.

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