
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
The convex quadrilateral  $ABCD$  has area  $1$ , and  $AB$  is produced to  $E$ ,  $BC$  to  $F$ ,  $CD$  to  $G$  and  $DA$  to  $H$ , such that  $AB=BE$ ,  $BC=CF$ ,  $CD=DG$  and  $DA=AH$ . Find the area of the quadrilateral  $EFGH$ .

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