
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
In triangle \(ABC\), lines parallel to the sides of the triangle are drawn through an arbitrary point \(O\). As a result, triangle \(ABC\) is divided into three parallelograms and three triangles. The areas of the resulting triangles are \(6 \, \text{cm}^2\), \(24 \, \text{cm}^2\), and \(54 \, \text{cm}^2\). Find the area of triangle \(ABC\).

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