
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
Suppose the function \( g(x) \) is defined for \( x \in \{a, b, c\} \) such that the points \( (a, g(a)), (b, g(b)), (c, g(c)) \) form a triangle with an area of \( 24 \). The graph of \( y = 3g(3x) \) likewise contains just three points. Determine the area of this triangle.

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