
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 two lines $l_1: x+y-3m=0$ and $l_2: 2x-y+2m-1=0$, their intersection point is $M$. If the y-intercept of line $l_1$ is 3,  
(Ⅰ) Find the coordinates of point $M$;  
(Ⅱ) Find the equation of the line that passes through point $M$ and is perpendicular to line $l_2$.

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