
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 rectangular coordinate system $(xOy)$, the equations of the ellipses $(C_{1})$ and $(C_{2})$ are given by $( \frac{x^{2}}{4}+y^{2}=1)$ and $( \frac{y^{2}}{16}+ \frac{x^{2}}{4}=1)$ respectively. The ray $(OA)$ intersects $(C_{1})$ and $(C_{2})$ at points $A$ and $B$ respectively, with $( \overrightarrow{OB}=2 \overrightarrow{OA})$. Find the slope of the ray $(OA)$.

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