
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]


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Given an ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) where \(a > b > 0\), and the point of intersection with the positive direction of the y-axis is \(A\). Find the number of isosceles right triangles inscribed in the ellipse with \(A\) as the vertex of the right angle.

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