
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 an ellipse $C: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ passing through the point $(1, \frac{3}{2})$, and the eccentricity $e= \frac{1}{2}$.
(I) Find the standard equation of the ellipse $C$;
(II) If line $l$: $y=kx+m$ intersects with the ellipse $C$ at two points $A$ and $B$ ($A$ and $B$ are not the left and right vertices), the right vertex of the ellipse is $D$, and $\overrightarrow{DA}\cdot \overrightarrow{DB}=0$, determine whether the line $l$ passes through a fixed point, if so, find the coordinates of the fixed point; if not, explain the reason.

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