
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 parametric equation of curve $C_{1}$ is $\begin{cases} x=\sqrt{3}+2\cos \alpha \\ y=2+2\sin \alpha \end{cases}(\alpha$ is the parameter$)$, and the equation of line $C_{2}$ is $y=\dfrac{\sqrt{3}}{3}x$. Establish a polar coordinate system with $O$ as the pole and the non-negative half-axis of $x$ as the polar axis.

  

$(1)$ Find the polar equations of curve $C_{1}$ and line $C_{2}$;

$(2)$ If line $C_{2}$ intersects curve $C_{1}$ at points $P$ and $Q$, find the value of $|OP|\cdot|OQ|$

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