
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 lines $l_{1}: 3x+2y-1=0$, $l_{2}: 5x+2y+1=0$, and $l_{3}: 3x-5y+6=0$, line $L$ passes through the intersection point of lines $l_{1}$ and $l_{2}$, and is perpendicular to line $l_{3}$. Find the general form equation of line $L$.

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