
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 $\frac{\sqrt{3}}{2}$, the area of the rhombus formed by connecting the ellipse's four vertices is $4$.

(1) Find the equation of the ellipse;

(2) A line $l$ intersects the ellipse at two distinct points $A$ and $B$, with point $A$ having coordinates $(-a,0)$ and $|AB|=\frac{4\sqrt{2}}{5}$. Find the angle of inclination of line $l$.

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