
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
In the Cartesian coordinate plane $(xOy)$, given points $M(-1,1)$, $N(0,2)$, and $Q(2,0)$.
(1) Find the standard equation of the circle $(C_{1})$ passing through points $M$, $N$, and $Q$.
(2) Circle $(C_{2})$ is the reflection of circle $(C_{1})$ about the line $MN$. Find the standard equation of circle $(C_{2})$.

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