
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 \(\Gamma: \frac{x^{2}}{4} + y^{2} = 1\), a line passing through the right focus \(F\) with a non-zero slope intersects the ellipse \(\Gamma\) at points \(A\) and \(B\). If \(AO^2 = AB\), then the coordinates of point \(A\) are \(\qquad\).

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