
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 line $C\_1$ is $\begin{cases} x=1+t \ y=2+t \end{cases} (t \text{ is the parameter})$, and in the polar coordinate system with origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the equation of circle $C\_2$ is $ρ=-2\cos θ+2 \sqrt {3}\sin θ$.
(I) Find the general equation of line $C\_1$ and the polar coordinates of the center of circle $C\_2$;
(II) Let points $A$ and $B$ be the intersection of line $C\_1$ and circle $C\_2$, find the length of chord $AB$.

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