
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
Consider rectangle  $ABCD$  with  $AB = 6$  and  $BC = 8$ .  Pick points  $E, F, G, H$  such that the angles  $\angle AEB, \angle BFC, \angle CGD, \angle AHD$  are all right.  What is the largest possible area of quadrilateral  $EFGH$ ?

*Proposed by Akshar Yeccherla (TopNotchMath)*

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