
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 $C:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1 (a > b > 0)$ with eccentricity $\dfrac{\sqrt{3}}{2}$, and the ellipse $C$ passes through point $A(1,-\dfrac{\sqrt{3}}{2})$. The line $l:y=x+m$ intersects the ellipse at two distinct points $A$ and $B$,

$(1)$ Find the equation of ellipse $C$;

$(2)$ If the area of $\Delta AOB$ is $1$ ($O$ is the origin), find the equation of line $l$.

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