
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 $⊙O$ with equation $x^{2}+y^{2}=6$, let $P$ be a moving point on the circle. Draw a line $PM$ perpendicular to the x-axis at point $M$, and let $N$ be a point on $PM$ such that $\overrightarrow{PM}= \sqrt {2} \overrightarrow{NM}$.

(I) Find the equation for the trajectory of point $N$, denoted as curve $C$.

(II) Given points $A(2,1)$, $B(3,0)$, if a line passing through point $B$ intersects curve $C$ at points $D$ and $E$, determine whether the sum of slopes $k_{AD}+k_{AE}$ is a constant value. If it is, find this value; if not, explain why.

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