
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
How many distinct $4 \times 4$ square shapes, that can be formed using eight $2 \times 1$ rectangles as shown, have both diagonals as axes of symmetry? Two square shapes are considered the same if they can be transformed into one another through rotation.

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