
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 square and  $O$  is your center. Let  $E,F,G,H$  points in the segments  $AB,BC,CD,AD$  respectively, such that  $AE = BF = CG = DH$ . The line  $OA$  intersects the segment  $EH$  in the point  $X$ ,  $OB$  intersects  $EF$  in the point  $Y$ ,  $OC$  intersects  $FG$  in the point  $Z$  and  $OD$  intersects  $HG$  in the point  $W$ . If the  $(EFGH) = 1$ . Find: $(ABCD) \times (XYZW)$ Note  $(P)$  denote the area of the polygon  $P$ .

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