
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. Let  $E, Z$  be points on the sides  $AB, CD$  of the square respectively, such that  $DE\parallel BZ$ . Assume that the triangles  $\triangle EAD, \triangle ZCB$  and the parallelogram  $BEDZ$  have the same area. 

If the distance between the parallel lines  $DE$  and  $BZ$  is equal to  $1$ , determine the area of the square.

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