
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 a rectangle  $ABCD, E$  is the midpoint of  $AB, F$  is a point on  $AC$  such that  $BF$  is perpendicular to  $AC$ , and  $FE$  perpendicular to  $BD$ . Suppose  $BC = 8\sqrt3$ . Find  $AB$ .

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