
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 rectangle with an area of 4. Let \(I\) be the midpoint of \([AD]\) and \(J\) be the midpoint of \([BC]\). Let \(X\) be the intersection point of \(AJ\) and \(BI\), and let \(Y\) be the intersection point of \(DJ\) and \(CI\). What is the area of the quadrilateral \(IXJY\)?

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