
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]


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Given points $M(4,0)$ and $N(1,0)$, any point $P$ on curve $C$ satisfies: $\overset{→}{MN} \cdot \overset{→}{MP} = 6|\overset{→}{PN}|$.

(I) Find the trajectory equation of point $P$;

(II) A line passing through point $N(1,0)$ intersects curve $C$ at points $A$ and $B$, and intersects the $y$-axis at point $H$. If $\overset{→}{HA} = λ_1\overset{→}{AN}$ and $\overset{→}{HB} = λ_2\overset{→}{BN}$, determine whether $λ_1 + λ_2$ is a constant value. If it is, find this value; if not, explain the reason.

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