
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
In the rectangular coordinate system, line $n$ passes through point $Q(\sqrt{3}, 4\sqrt{3})$ and is perpendicular to line $m$: $x + 2y = 0$. Line $n$ intersects the $x$-axis at point $M$, and point $M$ is symmetric to point $N$ about the $y$-axis. A moving point $P$ satisfies $|PM| + |PN| = 4$.

(I) Find the equation of the trajectory $C$ of moving point $P$;
(II) Line $l$ passes through point $D(1, 0)$ and intersects trajectory $C$ at points $A$ and $B$. Let point $E(4, 1)$, and let the slopes of lines $AE$ and $BE$ be $k_1$ and $k_2$, respectively. Determine whether $k_1 + k_2$ is a constant value. If it is, find this constant value; if not, explain why.

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