
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 equation of the line $l$ that passes through the intersection of lines $l_1: 3x+2y-1=0$ and $l_2: 5x+2y+1=0$,  
(1) and is parallel to the line $l_3: 3x-5y+6=0$;  
(2) and has equal intercepts on the x-axis and y-axis;  
(3) and when the area of the triangle formed by line $l$ with the negative x-axis and the positive y-axis is minimized, find the equation of line $l$.

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