
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 $E$: $mx^{2}+y^{2}=1$ ($m > 0$).
- (I) If the right focus of the ellipse $E$ is at $(\sqrt{3},0)$, find the value of $m$.
- (II) A triangle formed by three distinct points on the ellipse $E$ is called an inscribed triangle of the ellipse. If there are exactly three isosceles right-angled triangles inscribed in ellipse $E$ with $B(0,1)$ as the right-angle vertex, find the range of values for $m$.

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