
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
(Ⅰ) Find the equation of the line parallel to the line $x-2y+1=0$ and at a distance of $2\sqrt{5}$ from it;  
(Ⅱ) Find the equation of the line $l$ that passes through the intersection point $P$ of two lines $l_1: x-2y+4=0$ and $l_2: x+y-2=0$, and is perpendicular to the line $l_3: 2x+3y+1=0$.

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