
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 goes through $P = (-2, -3)$. Line $l_2$ has equation $y = 2$ and meets line $l_1$ at point $Q$. Line $l_3$ has positive slope, passes through point $P$, and meets $l_2$ at point $R$. The area of $\triangle PQR$ is $6$. What is the slope of $l_3$?

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