
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 $2 \times 2$ square can be cut into a small square and an L-shaped piece (corner) in four ways. All ways of cutting are shown in the picture below.

How many ways are there to cut a $4 \times 4$ square into three L-shaped pieces (corners) and a small square, as depicted in the picture? (Methods that differ by rotation or reflection of the square are considered distinct.)

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