
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 that the origin $O$ of the rectangular coordinate system is the pole, the positive semi-axis of the $x$-axis is the polar axis, and both coordinate systems have the same unit length. The parametric equation of line $l$ is $ \begin{cases} x= \frac {1}{2}t \\ y=3+ \frac { \sqrt {3}}{2}t \end{cases} (t \text{ is the parameter}) $, and the polar coordinate equation of curve $C$ is $ρ\cos ^{2}θ=4\sin θ$.

(1) Write the ordinary equation of line $l$ and the rectangular coordinate equation of curve $C$.
(2) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, and $M$ is the midpoint of $AB$. Point $P$ has polar coordinates $(4 \sqrt {3}, \frac {π}{3})$. Find the value of $|PM|$.

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