
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
 Parallelogram  $ABCD$  is given such that  $\angle ABC$  equals  $30^o$  . Let  $X$  be the foot of the perpendicular from  $A$  onto  $BC$ , and  $Y$  the foot of the perpendicular from  $C$  to  $AB$ . If  $AX = 20$  and  $CY = 22$ , find the area of the parallelogram.


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