
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 an ellipse \(\frac{x^{2}}{a^{2}} + y^{2} = 1\) with \(a > 1\), point \(B(0, 1)\) is the endpoint of the minor axis. A right-angled isosceles triangle \(\triangle ABC\) is inscribed in the ellipse with \(B\) as the vertex of the right angle. If there is only one such triangle, find the range of the real number \(a\).

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