
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 the parallelogram  $ABCD$ , a line through  $C$  intersects the diagonal  $BD$  at  $E$  and  $AB$  at  $F$ . If  $F$  is the midpoint of  $AB$  and the area of  $\vartriangle BEC$  is  $100$ , find the area of the quadrilateral  $AFED$ .

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