
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 $l$ passing through point $P(-2, 1)$.
(1) When the distance from line $l$ to points $B(-5, 4)$ and $C(3, 2)$ is equal, find the equation of line $l$;
(2) When the area of the triangle formed by line $l$ with the x-axis and y-axis is $\frac{1}{2}$, find the equation of line $l$.

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