
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 that passes through the intersection point M of lines $l_1: 3x+4y+5=0$ and $l_2: 2x-3y-8=0$, and satisfies the following conditions:
(1) Passes through the origin;
(2) Parallel to the line $2x+y+5=0$;
(3) Perpendicular to the line $2x+y+5=0$.

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