
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 \( 4x - 3y = 2 \) and passes through \( A = (-2, -3) \). Line \( l_2 \) has equation \( y = 2 \) and intersects line \( l_1 \) at point \( B \). Line \( l_3 \) has a positive slope, goes through point \( A \), and intersects \( l_2 \) at point \( C \). The area of \( \triangle ABC \) is \( 6 \). Find the slope of \( l_3 \).

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