
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
Given an ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)$ with eccentricity $e$, passing through the points $(2,0)$ and $(1,e)$.  
$(1)$ Find the equation of the ellipse $E$;  
$(2)$ If two lines $l_{1}$ and $l_{2}$ pass through $M(1,0)$, with slopes being reciprocals of each other, $l_{1}$ intersects ellipse $E$ at points $A$ and $B$, and $l_{2}$ intersects ellipse $E$ at points $C$ and $D$, where $P$ and $Q$ are the midpoints of $AB$ and $CD$ respectively. Investigate whether the ratio of the areas of $\triangle OPQ$ and $\triangle MPQ$ is a constant value. If it is, find this constant value; if not, explain the reason.

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