
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
In the Cartesian coordinate system $xOy$, the equation of curve $C$ is $x^{2}-2x+y^{2}=0$. Taking the origin as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of line $l$ is $\theta= \dfrac {\pi}{4}(\rho\in\mathbb{R})$.  
(Ⅰ) Write the polar equation of $C$ and find the polar coordinates of the intersection points $M$ and $N$ of $l$ and $C$;  
(Ⅱ) Let $P$ be a moving point on the ellipse $\dfrac {x^{2}}{3}+y^{2}=1$, find the maximum area of $\triangle PMN$.

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