
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 that point $P$ is a moving point on the circle $x^2+y^2=18$, and $PQ \perp x$-axis at point $Q$, if the moving point $M$ satisfies $\overrightarrow{OM}=\frac{1}{3}\overrightarrow{OP}+\frac{2}{3}\overrightarrow{OQ}$.

(Ⅰ) Find the equation of the trajectory $C$ of the moving point $M$;

(Ⅱ) The line passing through point $E(-4,0)$ with equation $x=my-4$ $(m\ne 0)$ intersects the curve $C$ at points $A$ and $B$. The perpendicular bisector of segment $AB$ intersects the $x$-axis at point $D$. Find the value of $\frac{|DE|}{|AB|}$.

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