
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 diagram below shows a parallelogram ABCD with  $AB = 36$  and  $AD = 60$ . Diagonal BD is
perpendicular to side AB. Points E and F bisect sides AD and BC, respectively. Points G and H are the
intersections of BD with AF and CE, respectively. Find the area of quadrilateral EGFH The diagram below shows a parallelogram ABCD with AB = 36 and AD = 60. Diagonal BD is
perpendicular to side AB. Points E and F bisect sides AD and BC, respectively. Points G and H are the
intersections of BD with AF and CE, respectively. Find the area of quadrilateral EGFH.

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