
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
Given that the graphs of the linear functions $y=\frac{3}{2}x+m$ and $y=-\frac{x}{2}+n$ both pass through the point $A(-4,0)$ and intersect the $y$-axis at points $B$ and $C$ respectively, calculate the area of $\triangle ABC$.

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