
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 that the intersection point of the lines $l_{1}$: $x-2y+3=0$ and $l_{2}$: $2x+3y-8=0$ is $M$, find the general equation of the line $l$ passing through point $M$ and perpendicular to the line $l_{3}$: $3x-y+1=0$.

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