
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 on the plane, with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar coordinate equation of line $l$ is given by $\rho \sin (\theta + \frac{\pi }{6})=1$, and the parametric equation of circle $C$ is given by $\begin{cases} & x=2+2\cos \theta \\ & y=-\sqrt{3}+2\sin \theta \end{cases}$ ($\theta$ is the parameter). Find the length of the chord obtained by the intersection of line $l$ and circle $C$.

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