
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
On the unit square \(ABCD\), the points \(A_1, B_1, C_1, D_1\) are marked such that \(AA_1 = BB_1 = CC_1 = DD_1 = \frac{1}{5}\). The points \(A\) and \(C_1\), \(B\) and \(D_1\), \(C\) and \(A_1\), \(D\) and \(B_1\) are then connected. What is the area of the small quadrilateral formed by these intersecting lines?

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