
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 trapezoid \(ABCD\), \(AD\) is parallel to \(BC\) and \(BC : AD = 5 : 7\). Point \(F\) lies on \(AD\) and point \(E\) lies on \(DC\) such that \(AF : FD = 4 : 3\) and \(CE : ED = 2 : 3\). If the area of quadrilateral \(ABEF\) is 123, determine the area of trapezoid \(ABCD\).

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