
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 of point $A$;

(II) Let $Q$ be a point on the locus. The circle through $QBC$ is externally tangent to the $x$-axis at point $O_1$. Find the minimum distance from point $O_1$ to the $x$-axis as $Q$ moves along the locus.

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