
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 $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)$ with eccentricity $e=\frac{\sqrt{6}}{3}$, and a line $l:y=kx+m$ intersecting the ellipse at points $B$ and $C$. When the equation of the line $l$ is $y=\sqrt{3}x-3$, it passes through one of the vertices of the ellipse's major axis.  
$(1)$ Find the equation of $E$;  
$(2)$ Let the origin be $O$, and there exists a point $A(p,q)$ on $E$ other than $B$ and $C$, satisfying $\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}=0$. Determine whether the area of $\triangle ABC$ is a constant value. If it is a constant value, find the value; if not, explain the reason.

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