
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 a line $l$ passing through the point $P(0,-1)$ with its parametric equation as $\begin{cases} x= \frac {1}{2}t \\ y=-1+ \frac { \sqrt {3}}{2}t\end{cases}$ (where $t$ is the parameter), in the polar coordinate system with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, the equation of curve $C$ is $2a\sin \theta-\rho\cos ^{2}\theta=0$ ($a > 0$).  
(Ⅰ) Find the rectangular coordinate equation of curve $C$;  
(Ⅱ) If line $l$ intersects curve $C$ at points $M$ and $N$, and $|PM|$, $|MN|$, $|PN|$ form a geometric progression, find the value of $a$.

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