
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 \(\frac{x^{2}}{2} + y^{2} = 1\), let \(M\) be any point on the circle \(x^{2} + y^{2} = 3\). \(M A\) and \(M B\) are tangent to the ellipse \(C\) at points \(A\) and \(B\), respectively. Find the range of the area of \(\triangle O A B\) (where \(O\) is the origin).

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