
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
A trapezoid has a base of length \(a\), a parallel side of length \(b\), and a height \(m\). The height is divided into three equal parts of length \(s\), and lines parallel to the base are drawn through the division points. What are the areas of the trapezoids thus formed?

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