
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
A circle passes through three vertices of the ellipse $\frac{x^{2}}{4}+y^{2}=1$ and its center lies on the positive semi-axis of $x$. Determine the standard equation of the circle.

A) $(x-\frac{3}{2})^{2}+y^{2}=\frac{25}{4}$
B) $(x+\frac{3}{4})^{2}+y^{2}=\frac{25}{16}$
C) $(x-\frac{3}{4})^{2}+y^{2}=\frac{25}{16}$
D) $(x-\frac{3}{4})^{2}+y^{2}=\frac{25}{4}$

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