
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
Divide the sides of a unit square \(ABCD\) into 5 equal parts. Let \(D'\) denote the second division point from \(A\) on side \(AB\), and similarly, let the second division points from \(B\) on side \(BC\), from \(C\) on side \(CD\), and from \(D\) on side \(DA\) be \(A'\), \(B'\), and \(C'\) respectively. The lines \(AA'\), \(BB'\), \(CC'\), and \(DD'\) form a quadrilateral.

What is the area of this quadrilateral?

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