
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 points A (-3, 0), B (3, 0), and a moving point P satisfying $|PA| = 2|PB|$.  
(1) If the trajectory of point P is curve C, find the equation of curve C;  
(2) If point Q is on the line $l_1: x + y + 3 = 0$, and line $l_2$ passes through point Q and has only one common point M with curve C, when $|QM|$ is minimized, find the equation of line QM.

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