
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 in the rectangular coordinate system $(xOy)$, the parametric equation of line $l$ is $ \begin{cases} x=-3t\\y=m+ \sqrt {3}t \end{cases}$ ($t$ is the parameter, $m$ is a constant), and the polar coordinate system is established with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of curve $C$ is $\rho=a\sin (\theta+ \frac {\pi}{3})$. Point $M$ has polar coordinates $(4, \frac {\pi}{6})$ and lies on curve $C$.

(I) Find the value of $a$ and the rectangular coordinate equation of curve $C$;

(II) If point $M$ is symmetric about line $l$ to point $N$ on curve $C$, find the length of $|MN|$.

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