
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 lines $l\_1$: $2x-3y+1=0$, $l\_2$: $x+y-2=0$ intersect at point $P$.
(1) Find the coordinates of point $P$;
(2) Find the equation of line $l$ that passes through point $P$ and is perpendicular to line $l\_2$.

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