
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 points $A(4,0)$ and $B(0,3)$, find the general equation of line $l_1$ such that:  
(1) $l_1 \parallel l$, and passes through the intersection point of the two lines $3x+y=0$ and $x+y=2$;  
(2) $l_1 \perpendicular l$, and the triangle formed by $l_1$ and the coordinate axes has an area of 6.

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