
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 the ellipse $C$: $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)$ with its left focus at $F(-2,0)$ and eccentricity $\dfrac{\sqrt{6}}{3}$.

(Ⅰ) Find the standard equation of the ellipse $C$;  
(Ⅱ) Let $O$ be the origin of coordinates, and $T$ be a point on the line $x = -3$. A perpendicular line from $F$ to $TF$ intersects the ellipse at points $P$ and $Q$. When the quadrilateral $OPTQ$ forms a parallelogram, find the area of the quadrilateral $OPTQ$.

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