
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 three lines $l_{1}$: $x+y-2=0$, $l_{2}$: $x-3y+10=0$, $l_{3}$: $3x-4y+5=0$.  
$(Ⅰ)$ Find the coordinates of the intersection point $M$ of lines $l_{1}$ and $l_{2}$.  
$(Ⅱ)$ Find the equation of the line passing through point $M$ and parallel to line $l_{3}$.  
$(Ⅲ)$ Find the equation of the line passing through point $M$ and perpendicular to line $l_{3}$.

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