
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 $xOy$, the vertex of parabola $C$ is at the origin and the parabola passes through point $A(2,2)$, with its focus $F$ on the $x$-axis.  
(Ⅰ) Find the equation of the line that passes through point $F$ and is perpendicular to line $OA$.  
(Ⅱ) Suppose a line passing through point $M(m,0)$ (where $m > 0$) intersects the parabola $C$ at points $D$ and $E$, and $|ME|=2|DM|$, find the minimum value of $\frac {|DE|^2+1}{|OM|}$.

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