
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
In the diagram, \(EFGH\) is a rectangle with dimensions \(EF = 8\) and \(EH = 4\), and \(IJKL\) is a rectangle with \(IL = 12\) and \(IK = 4\). Also, \(GH\) and \(IJ\) are perpendicular. The shaded area within \(IJKL\) is equal to three-quarters of the area of \(EFGH\). Determine the length of \(EI\).

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