
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 $l_1: x-2y+4=0$ and $l_2: x+y-2=0$ intersecting at point $P$,

(1) Find the coordinates of the intersection point $P$;
(2) Let line $l_3: 3x-4y+5=0$. Find the equations of the lines passing through point $P$ that are parallel and perpendicular to line $l_3$ respectively.

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