
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 $\dfrac {\sqrt {6}}{3}$, which passes through point $M(-3,-1)$.  
(Ⅰ) Find the equation of ellipse $C$.  
(Ⅱ) If a line $l$: $x-y-2=0$ intersects the ellipse $C$ at points $A$ and $B$, and point $P$ is a moving point on ellipse $C$ such that the area of $\triangle PAB$ is maximized, find the coordinates of point $P$ and the maximum area of $\triangle PAB$.

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