
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 the parabola $C: x^{2}=2y$ with focus $F$, draw the tangent line $l$ to the parabola at a point $M$ on $C$, and let $l$ intersect the $y$-axis at point $N$.

(1) Determine the shape of $\triangle MFN$;
(2) If points $A$ and $B$ are on parabola $C$, and point $D(1,1)$ satisfies $\overrightarrow{AD} + \overrightarrow{BD} = \overrightarrow{0}$, and if there exists a point $E$ on parabola $C$, different from $A$ and $B$, such that the circle passing through points $A$, $B$, and $E$ has the same tangent as parabola $C$ at point $E$, find the coordinates of point $E$.

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