
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
In the Cartesian coordinate system $xy$, a circle with center O is tangent to the line $x - \sqrt{3}y = 4$.
(I) Find the equation of circle O.
(II) The circle O intersects the x-axis at points A and B. A moving point P $(x_0, y_0)$ inside the circle satisfies $|PO|^2 = |PA| \cdot |PB|$. Determine the range of values for $x_0^2 + y_0^2$.

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