
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
The standard equation of the circle passing through the point $(-2,4)$ and intersecting with circles $C_{1}$: $x^{2}+y^{2}-2x=0$ and $C_{2}$: $x^{2}+y^{2}-2y=0$ is $(x-1)^{2}+(y+2)^{2}=5$.

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