
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 triangle $ABC$, where $B(-1,0)$, $C(1,0)$, and $|AB|+|AC|=4$.
(I) Find the equation of the locus $M$ of moving point $A$;
(II) Let $P$ be a point on the locus $M$, and the circumcircle of triangle $PBC$ be $⊙O_{1}$ ($O_{1}$ being the center), find the minimum distance from point $O_{1}$ to the $x$-axis as $P$ moves on $M$.

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