
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 that $M$ is any point on the ellipse $\frac{x^{2}}{4}+y^{2}=1$, $N$ is the projection of point $M$ on the line $x=3$, and $\overrightarrow{OP}=\overrightarrow{OM}+\overrightarrow{ON}$, where $O$ is the coordinate origin.
(I) Find the equation of the trajectory $E$ of moving point $P$;
(II) The line $l$ passing through point $A(1,4)$ is tangent to the curve $E$ found in part (I). Find the equation of the tangent line $l$.

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