
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
Let  $ABCD$  be a rhombus of sides  $AB = BC = CD= DA = 13$ . On the side  $AB$  construct the rhombus   $BAFC$  outside  $ABCD$  and such that the side  $AF$   is parallel to the diagonal  $BD$  of  $ABCD$ . If the area of  $BAFE$  is equal to  $65$ , calculate the area of  $ABCD$ .

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