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

1. Find the trajectory equation of point $P$.
2. 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 $\overrightarrow{HA} = λ_{1} \overrightarrow{AN}$ and $\overrightarrow{HB} = λ_{2} \overrightarrow{BN}$, 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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