
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 a circle $O: x^2 + y^2 = 6$, and $P$ is a moving point on circle $O$. A perpendicular line $PM$ is drawn from $P$ to the x-axis at $M$, and $N$ is a point on $PM$ such that $\overrightarrow{PM} = \sqrt{2} \overrightarrow{NM}$.

(Ⅰ) Find the equation of the trajectory $C$ of point $N$;  
(Ⅱ) If $A(2,1)$ and $B(3,0)$, and a line passing through $B$ intersects curve $C$ at points $D$ and $E$, is $k_{AD} + k_{AE}$ a constant value? If yes, find this value; if not, explain why.

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