
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 that the ratio of the distance from point M to point A(-2, 0) and point B(1, 0) is equal to 2, denote the trajectory of point M as curve C.

(1) Find the equation of curve C;

(2) Draw a tangent line to curve C passing through point P(4, -4), and find the equation of the tangent line.

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