
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
It is known that the lines $2x-y-1=0$ and $x-2y+1=0$ intersect at point P.  
(1) Find the equation of line $l_1$ that passes through point P and is perpendicular to the line $3x+4y-15=0$. The result should be in the general form of a line equation.  
(2) Find the equation of line $l_2$ that passes through point P and has equal intercepts on both coordinate axes. The result should be expressed in the general form of a line equation.

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