
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 moves on the circle $x^2+y^2=1$, and DP is perpendicular to the y-axis with the foot of the perpendicular being point D. Point M is on line segment DP, and $\frac {|DM|}{|DP|}=\frac {\sqrt {2}}{2}$.  
(Ⅰ) Find the equation of the trajectory of point M;  
(Ⅱ) Line l intersects the y-axis at point Q(0, m) (m ≠ 0) and intersects with the trajectory of point M at distinct points A and B. Vector $\overrightarrow{AQ}$ is λ times $\overrightarrow{QB}$, and if $\overrightarrow{OA} + \lambda \overrightarrow{OB} = 4\overrightarrow{OQ}$. Find the range of the values of m.

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