
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
In a Cartesian coordinate system \(xy\), consider an ellipse \(\Gamma: \frac{x^{2}}{9}+y^{2}=1\) and a rhombus \(ABCD\) where points \(A\), \(B\), \(C\), and \(D\) lie on the ellipse \(\Gamma\). The diagonals \(AC\) and \(BD\) intersect at the origin \(O\).

(1) Find the minimum possible area of the rhombus \(ABCD\).

(2) Is there a specific circle that is tangent to any rhombus \(ABCD\) that meets the given conditions? If so, find the equation of such a circle; if not, explain why.

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