
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 Cartesian coordinate system $xOy$, the equation of the line $l$ is $y=\sqrt{3}x$. A polar coordinate system is established with the origin as the pole and the positive x-axis as the polar axis. The polar coordinate equation of the curve $C$ is $\rho \cos ^{2}\theta =8\sin \theta $.<br/>$(1)$ Find the Cartesian equation of the curve $C$;<br/>$(2)$ Given that the line $l$ intersects the curve $C$ at points $O$ and $P$, find the polar coordinates $\left(\rho ,\theta \right)\left(\rho\ \ \gt 0,\theta \in \left[0,2\pi \right)\right)$ of the midpoint $N$ of the line segment $OP$.

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