
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 $XOY$, there is a line $l:\begin{cases} & x=t \\ & y=-\sqrt{3}t \\ \end{cases}(t$ is a parameter$)$, and a curve ${C_{1:}}\begin{cases} & x=\cos \theta \\ & y=1+\sin \theta \\ \end{cases}(\theta$ is a parameter$)$. Establish a polar coordinate system with the origin $O$ of this rectangular coordinate system as the pole and the non-negative half-axis of the $X$-axis as the polar axis. The equation of the curve ${C_{2}}$ is $\rho=4\sin (\theta -\frac{\pi }{6})$.

1. Find the polar coordinate equation of the curve ${C_{1}}$ and the rectangular coordinate equation of the curve ${C_{2}}$.
2. Suppose the line $l$ intersects the curve ${C_{1}}$ at points $O$ and $A$, and intersects the curve ${C_{2}}$ at points $O$ and $B$. Find the length of $|AB|$.

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