
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 circle M: x²+(y-1)²=16, there is a point A(4, -2) outside the circle. Draw a line l passing through point A.
(1) Find the equation of line l when it is tangent to circle M;
(2) Find the length of the chord formed by line l on circle M when the slope angle of line l is 135°.

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