
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  $ABC$  be a right triangle with hypotenuse  $\overline{AC}$  and circumcenter  $O$ . Point  $E$  lies on  $\overline{AB}$  such that  $AE = 9$ ,  $EB = 3$ ,  point  $F$  lies on  $\overline{BC}$  such that  $BF = 6$ ,  $FC = 2$ . Now suppose  $W, X, Y$ , and  $Z$  are the midpoints of  $\overline{EB}$ ,  $\overline{BF}$ ,  $\overline{FO}$ , and  $\overline{OE}$ , respectively. Compute the area of quadrilateral  $W XY Z$ .

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