
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
A $10 \times 10$ square was cut along the grid lines into 17 rectangles, each of which has both sides longer than 1. What is the smallest number of squares that could be among these rectangles? Provide an example of such a cutting.

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