
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, one can form a \(4 \times 4\) square. If one formed square is the same as another formed square after a rotation, then the two formed squares are considered the same. Among all possible formed square patterns, how many patterns are there that are symmetric about the horizontal axis and have two adjacent blank small squares in the first row?

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