
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 \( C_1: \frac{x^{2}}{4} + y^{2} = 1 \) and the ellipse \( C_2: (x - 2)^{2} + 4y^{2} = 1 \), the common tangent to \( C_1 \) and \( C_2 \) intersects the x-axis at point \( A \). Determine the coordinates of point \( A \).

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