
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, the parametric equation of the ellipse $C$ is $\begin{cases} x=2\cos \theta \\ y=\sin \theta \end{cases}$ (where $\theta$ is the parameter), given that the polar coordinate system is established with the origin as the pole and the positive half of the $x$-axis as the polar axis, the polar equation of ray $l$ is $\theta=\alpha$ ($\rho \geqslant 0$, note: for this problem, $\rho \geqslant 0$, $\theta \in [0,2\pi)$): 
(1) Convert the parametric equations of ellipse $C$ to polar coordinates;  
(2) Suppose ray $l$ intersects ellipse $C$ at point $A$, then rotate ray $l$ counterclockwise by $90^{\circ}$, resulting in ray $OB$ intersecting ellipse $C$ at point $B$. Determine whether $\dfrac{1}{|OA|^2}+ \dfrac{1}{|OB|^2}$ is a constant value. If it is, find the constant. If not, explain why.

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