
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 (x, y) satisfying $|\overrightarrow{PA}| = 2|\overrightarrow{PB}|$  
(1) Find the equation of the trajectory C of point P;  
(2) If a line $l$ is parallel to $x+y+3=0$ and tangent to C, find the equation of $l$.

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