
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
The ellipse $E$: $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ has its left and right foci as $F_{1}$ and $F_{2}$, respectively. $D$ is a vertex on the short axis of the ellipse, and the extension line of $DF_{1}$ intersects the ellipse at $G$. The perimeter of $\triangle DGF_{2}$ is $8$, and $|DF_{1}|=3|GF_{1}|$.  
(Ⅰ) Find the equation of the ellipse $E$;  
(Ⅱ) Through the left vertex $A$ of the ellipse $E$, draw two mutually perpendicular chords $AB$ and $AC$ of the ellipse $E$. Determine whether the line $BC$ always passes through a fixed point. If so, find the coordinates of this fixed point; if not, please explain why.

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