
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 lines $2x+y-8=0$ and $x-2y+1=0$ intersect at point $P$.
(1) Find the equation of the line $l_1$ that passes through point $P$ and is parallel to the line $4x-3y-7=0$. (Express the result in general form)
(2) Find the equation of the line $l_2$ that passes through point $P$ and maximizes the distance from the origin $O$ to this line.

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