
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 $3x - 2y = 1$ and goes through point $A = (-1, -2)$. Line $l_2$ now has equation $y = 2$ and meets line $l_1$ at point $B$. Line $l_3$ has positive slope, goes through point $A$, and intersects $l_2$ at point $C$. Calculate the area of $\triangle ABC$ and determine the slope of $l_3$, given that the area is $5$ units².

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