
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 distance from the moving point $M(x,y)$ to the line $l: x=4$ is twice its distance to the point $N(1,0)$.
(1) Find the trajectory $C$ of the moving point $M$;
(2) The line $m$ passing through the point $P(0,3)$ intersects the trajectory $C$ at points $A$ and $B$. If $A$ is the midpoint of $PB$, find the slope of the line $m$.

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