
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 $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$, with an eccentricity of $\frac{1}{2}$. The area of the triangle formed by the origin, the intersection point of the line $x=1$ and the ellipse $C$ is $\frac{3}{2}$.
(1) Find the equation of the ellipse;
(2) If line $l$ passes through the point $(\frac{2}{7},0)$ and intersects the ellipse $C$ at points $A$ and $B$ ($A$ and $B$ are not the left and right vertices), and $D$ is the right vertex of the ellipse $C$, determine whether $\angle ADB$ is a fixed value.

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