
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
Points \(E, F, G, H\) lie on the sides of a larger square such that each divides the sides into segments that are in the ratio 1:2 and 2:1 from one vertex. If the larger square has an area of 144 square units, what is the area of the quadrilateral formed by connecting the points \(E, F, G,\) and \(H\)?

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