
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 parallelogram with  $AB=8$ ,  $AD=11$ , and  $\angle BAD=60^\circ$ .  Let  $X$  be on segment  $CD$  with  $CX/XD=1/3$  and  $Y$  be on segment  $AD$  with  $AY/YD=1/2$ .  Let  $Z$  be on segment  $AB$  such that  $AX$ ,  $BY$ , and  $DZ$  are concurrent.  Determine the area of triangle  $XYZ$ .

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