
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
Given that in the square \(ABCD\), \(E\) is the midpoint of the side \(DC\), and the line segment \(BE\) intersects the diagonal \(AC\) at point \(F\), determine the area of the square \(ABCD\) if the area of the quadrilateral \(AFED\) is 45.

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