
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
Using eight $2 \times 1$ small rectangles as shown in the diagram, you can form a $4 \times 4$ square. If one assembled square, after rotating, is the same as another assembled square, they are considered identical. How many distinct squares can be formed where both diagonals are axes of symmetry?

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