
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
Two lines, parallel to the bases of a trapezoid, divide each of the lateral sides into three equal parts. The entire trapezoid is divided into three sections by these lines. Find the area of the middle section if the areas of the outer sections are \(S_{1}\) and \(S_{2}\).

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