
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), a curve ${C}_{1}:\begin{cases} & x=\cos \theta \\ & y=1+\sin \theta \\ \end{cases}$ ($\theta$ is a parameter), and a curve ${C}_{2}$ with the equation $\rho =-2\cos \theta +2\sqrt{3}\sin \theta$ in the polar coordinate system with the origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis.

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

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