
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
Line \( l_1 \) has equation \( 5x - 3y = 2 \) and goes through \( A = (2, -2) \). Line \( l_2 \) has equation \( y = 2 \) and meets line \( l_1 \) at point \( B \). Line \( l_3 \) has positive slope, goes through point \( A \), and meets \( l_2 \) at point \( C \). The area of \(\triangle ABC\) is \( 5 \). What is the slope of \( l_3 \)?

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