
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 the center of the ellipse $(C)$ is at the origin of the coordinate, the focus is on the $x$-axis, and the eccentricity is $\frac{1}{2}$, a line passes through the left focus $(F)$ of the ellipse at an angle of $60^{\circ}$ and is tangent to the circle $x^{2}+y^{2}= \frac{b^{2}}{a^{2}}$.
(I) Find the equation of the ellipse $(C)$;
(II) If the line $l$: $y=kx+m$ intersects the ellipse $(C)$ at two distinct points $M$ and $N$ ($M$ and $N$ are the left and right vertices, respectively), and the circle with $MN$ as the diameter passes through the right vertex $(A)$ of the ellipse $(C)$, 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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