
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 rectangular coordinate system $(xOy)$, the parametric equation of circle $C$ is $\begin{cases} x=\sqrt{3}+2\cos \theta, \\ y=2\sin \theta \end{cases}(\theta$ is the parameter$)$, and the parametric equation of line $m$ is $\begin{cases} x=\sqrt{3}+\frac{1}{2}t, \\ y=7+\frac{\sqrt{3}}{2}t \end{cases}(t$ is the parameter$)$. Establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis.

(1) Find the ordinary equation of circle $C$ and the polar coordinate equation of line $m$;

(2) Ray $l$: $y=-\frac{\sqrt{3}}{3}x$ $(x\leqslant 0)$, assume ray $l$ intersects circle $C$ at point $A$ and line $m$ at point $B$, find $|OA|\cdot|OB|$.

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