
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 $C$: $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)$, its right focus is $F(2,0)$, and point $P(2, \dfrac{\sqrt{6}}{3})$ is on the ellipse.
(Ⅰ) Find the equation of ellipse $C$;
(Ⅱ) A line passing through point $F$ intersects the ellipse $C$ at points $A$ and $B$. Point $M$ is on the ellipse $C$, and the origin $O$ is exactly the centroid of $\triangle ABM$. Find the equation of line $l$.

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