
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 line $2x-y-4=0$ intersects with the line $x-2y+1=0$ at point $P$.  
(1) Find the equation of line $l_1$ that passes through point $P$ and is perpendicular to the line $3x+4y-15=0$ (Write the result in the general form of the line equation).  
(2) Find the equation of line $l_2$ that passes through point $P$ and has equal intercepts on both coordinate axes (Write the result in the general form of the line equation).

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