
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
The side length of the large square \(ABCD\) is 10 centimeters, and the side length of the small square is 1 centimeter. As shown in the diagram, the small square slides along the side \(AB\) of the large square from \(A\) to \(B\), then slides from \(B\) along the diagonal \(BD\) to \(D\), and finally slides from \(D\) along the side \(DC\) to \(C\). The area swept by the small square is \(\quad\) square centimeters.

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