
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 scanning code consists of an $8 \times 8$ grid of squares, where some squares are colored black and others are colored white. Each code must have at least one square of each color. A scanning code is termed $\textit{symmetric}$ if it appears the same when the grid is rotated by multiples of 90 degrees or reflected across a line joining midpoints of opposite sides or a diagonal. How many such symmetric scanning codes can exist?

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