
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
1. Find the equation of the line that passes through the origin and the intersection point of the following two lines: $l_1: x-2y+2=0$, $l_2: 2x-y-2=0$;  
2. Find the equation of the circle whose center lies on the line $3x+4y-1=0$ and passes through the intersection points of the two circles $x^2+y^2-x+y-2=0$ and $x^2+y^2=5$.

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