
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 plane rectangular coordinate system $(xOy)$, establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of the curve $(C_{1})$ is $\rho \sin \theta =2$, and $M$ is a moving point on the curve $(C_{1})$. Point $P$ is on the line segment $OM$ and satisfies $|OM|\cdot |OP|=4$.
(1) Find the rectangular coordinate equation of the trajectory $(C_{2})$ of point $P$;
(2) The parametric equations of line $l$ are $\begin{cases} & x=t\cos \alpha \\ & y=t\sin \alpha \end{cases}(t\text{ is a parameter})$, where $0\leqslant \alpha < \pi$. Line $l$ intersects $(C_{2})$ at point $A$, and $|OA|=\sqrt{3}$. Find the slope of line $l$.

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