
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
Given the curves $C\_1: \begin{cases} x=1+cos⁡θ \ y=sin⁡θ \end{cases} (θ \text{ is a parameter})$ and $C\_2: \begin{cases} x=- \frac { \sqrt {3}}{2}t \ y= \frac {2 \sqrt {3}}{3}+ \frac {t}{2}\end{cases} (t \text{ is a parameter})$,

(1) Find the length of the line segment $|AB|$, where $A$ and $B$ are the intersection points of the curves $C\_1$ and $C\_2$.

(2) Establish a polar coordinate system with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis. A line $l\_1$ passing through the pole intersects curve $C\_1$ at points $O$ and $C$, and intersects the line $ρ\sin θ=2$ at point $D$. Find the maximum value of $\frac{|OC|}{|OD|}$.

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