
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 ellipse $C$: $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ $(a > b > 0)$ passes through the point $(1,\dfrac{3}{2})$, and its eccentricity $e=\dfrac{1}{2}$.

(I) Find the standard equation of the ellipse $C$;

(II) If the line $l$: $y=kx+m$ intersects the ellipse $C$ at points $A$ and $B$ (where $A,B$ are not the left and right vertices), and the right vertex of the ellipse is $D$, satisfying $\overrightarrow{DA} \cdot \overrightarrow{DB} = 0$, determine whether the line $l$ passes through a fixed point. If it does, find the coordinates of the fixed point; if not, explain why.

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