
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 intersection of lines $l_1: 2x+3y-5=0$ and $l_2: 7x+15y+1=0$, and is parallel to the line $x+2y-3=0$;  
(2) Find the equation of the line that is perpendicular to the line $3x+4y-7=0$ and has a distance of 6 from the origin.

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