
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 polar coordinate system, point $P$ is any point on the curve $C\_1$: $p=2\cos \theta$, and point $Q$ is on the ray $OP$, satisfying $|OP|\cdot|OQ|=6$. The trajectory of point $Q$ is denoted as curve $C\_2$.
(I) Find the rectangular coordinate equation of curve $C\_2$;
(II) Suppose line $l$: $\theta= \frac{\pi}{3}$ intersects $C\_1$ and $C\_2$ at points $A$ and $B$, respectively. Find $|AB|$.

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