
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 line $l$ passes through the intersection point $P$ of lines $l'$: $3x+4y-2=0$ and $2x+y+2=0$, and is perpendicular to the line $x-2y-1=0$.

(1) Find the equation of line $l$;

(2) Find the area $S$ of the triangle formed by lines $l$, $l'$ and the $x$-axis.

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