
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
Lines $l_1$ and $l_2$ are given by the equations $4x - 3y = 2$ and $y = 2$ respectively, and meet at point $B$. Line $l_3$ has a positive slope, passes through point $A = (0, -3)$, and intersects $l_2$ at point $C$. If the area of $\triangle ABC$ is $5$, find the slope of $l_3$.

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