
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
Let line $l_1$ be defined by the equation $2x + 3y = 6$ and pass through point $A = (3, 0)$. Line $l_2$ is defined by the equation $y = 2$ and intersects $l_1$ at point $B$. Line $l_3$ passes through point $A$ and also intersects $l_2$ at point $C$. The area of $\triangle ABC$ is $6$. Determine the slope of $l_3$.

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