
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  $\triangle{ADE}$  points  $B$  and  $C$  are on side  $AD$  and points  $F$  and  $G$  are on side  $AE$  so that  $BG \parallel CF \parallel DE$ , as shown. The area of  $\triangle{ABG}$  is  $36$ , the area of trapezoid  $CFED$  is  $144$ , and  $AB = CD$ . Find the area of trapezoid  $BGFC$ .

[center]![Image](https://snag.gy/SIuOLB.jpg)[/center]

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