
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 line $l$ passes through point $P(-1,2)$ and forms a triangle with the positive semi-axes of the coordinate axes, the area of which is $\frac{1}{2}$.  
$(1)$ Find the equation of line $l$.  
$(2)$ Find the equation of the circle whose center is on line $l$ and passes through points $M(2,1)$ and $N(4,-1)$.

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