
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
Find the standard equations of the following circles:  
(1) The center of the circle is on the line $y=0$, and the circle passes through two points $A(1,4)$ and $B(3,2)$;  
(2) The center of the circle is on the line $2x+y=0$, and the circle is tangent to the line $x+y-1=0$ at point $M(2,-1)$.

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