
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 its left and right foci being $F_{1}$ and $F_{2}$ respectively, and its eccentricity is $\dfrac {1}{2}$. Let $M$ be any point on the ellipse and the perimeter of $\triangle MF_{1}F_{2}$ equals $6$.

(Ⅰ) Find the equation of the ellipse $C$;  
(Ⅱ) With $M$ as the center and $MF_{1}$ as the radius, draw a circle $M$. When circle $M$ and the line $l$: $x=4$ have common points, find the maximum area of $\triangle MF_{1}F_{2}$.

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