
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 line $\sqrt {2}x-y+m=0$ does not pass through the origin and intersects the ellipse $\frac {y^{2}}{4}+ \frac {x^{2}}{2}=1$ at two distinct points A and B.  
(Ⅰ) Find the set M of all possible values of the real number m;  
(Ⅱ) Determine whether there exists a fixed point P such that for any $m \in M$, the angles of inclination of lines PA and PB are complementary. If such a point exists, find the coordinates of all such fixed points P; if not, explain why.

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