
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 a circle M: $x^2+y^2-4x+2y+c=0$ intersects the y-axis at points A and B, with the center at M, and $\angle AMB=90^\circ$.
(Ⅰ) Find the value of $c$;
(Ⅱ) If circle M intersects the line $x+y-1=0$ at points E and F, and the x-coordinate of E, $x_E$, is less than the y-coordinate of F, $y_F$, and a moving point H has the ratio of distances to points E and F as $\lambda$ ($\lambda>0$), find the equation of the trajectory of point H and explain what shape it is.

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