
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
The base of a triangle is $30 \text{ cm}$, and the other two sides are $26 \text{ cm}$ and $28 \text{ cm}$. The height of the triangle is divided in the ratio $2:3$ (counting from the vertex), and a line parallel to the base is drawn through the point of division. Determine the area of the resulting trapezoid.

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