
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 and the intersection points of $C$ with the line $x=1$ is $\frac{3}{2}$.  
(1) Find the equation of the ellipse;  
(2) If a line $l$ passes through the point ($\frac{2}{7}$, 0) and intersects the ellipse $C$ at points $A$ and $B$ (where $A$ and $B$ are not the left and right vertices), and $D$ is the right vertex of the ellipse $C$, find the constant value of $\angle ADB$.

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