
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 triangle ABC with B(-1, 0), C(1, 0), and |AB|+|AC|=4.  
(Ⅰ) Find the equation of the trajectory M of the moving point A;  
(Ⅱ) Let P be a moving point on trajectory M, and the circumcircle of △PBC is denoted as ⊙O<sub>1</sub> (O<sub>1</sub> being the center). When P moves on M, find the minimum distance from point O<sub>1</sub> to the x-axis.

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