
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 equations of curve $E$ are $\left\{{\begin{array}{l}{x=\sqrt{2}+cosα}\\{y=sinα}\end{array}}\right.$ ($\alpha$ is the parameter). Establish a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis. The ray $l_{1}$: $θ=β$ ($-\frac{π}{4}＜β＜0$) intersects $E$ at points $A$ and $B$, and the ray $l_{2}$: $θ=β+\frac{π}{4}$ intersects $E$ at points $C$ and $D$. <br/>$(1)$ Find the polar coordinate equation of curve $E$; <br/>$(2)$ Find the range of $\frac{{|{OC}|+|{OD}|}}{{|{OA}|+|{OB}|}}$.

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