
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 an arbitrary point on the ellipse $\frac{x^2}{4} + y^2 = 1$, and $N$ is the projection of point $M$ on the line $x=3$, and $\overrightarrow{OP} = \overrightarrow{OM} + \overrightarrow{ON}$, where $O$ is the origin of the coordinate system.
(I) Find the equation of the locus $E$ of the point $P$.
(II) The line $l$ passing through point $A(1, 4)$ is tangent to the curve $E$ from (I). Find the equation of the tangent line $l$.

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