
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 a circle $C$ with its center on the positive $x$-axis, and the point $(0, \sqrt{5})$ on circle $C$, and the distance from the center of the circle to the line $2x-y=0$ is $\dfrac{4\sqrt{5}}{5}$, then the equation of circle $C$ is \_\_\_\_\_\_.

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