
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 moving circle M passes through a fixed point A(2, 0) and cuts a chord of length 4 on the y-axis.

(Ⅰ) Find the equation of the trajectory C of the center M of the circle.

(Ⅱ) Let N$(x_0, 0)$ be a fixed point on the x-axis, and BD be any chord of the trajectory C passing through point N. If $\angle BAD$ is always obtuse, find the range of $x_0$.

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