
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 the ellipse $C$: $\frac{x^{2}}{4} + \frac{y^{2}}{m} = 1 (m > 0)$.
(I) If $m = 2$, find the eccentricity and the length of the minor axis of the ellipse $C$;
(II) If there exists a line $l$ passing through the point $P(-1, 0)$ and intersecting the ellipse $C$ at points $A$ and $B$, such that the circle with the segment $AB$ as its diameter passes through the origin, find the range of values for $m$.

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