
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, with some squares colored black and the rest white. There must be at least one square of each color. A scanning code is called $\textit{symmetric}$ if it appears the same when the entire grid is rotated by $90^{\circ}$, $180^{\circ}$, or $270^{\circ}$ counterclockwise around its center, and when it is reflected across any line joining midpoints of opposite sides or any diagonal line. How many possible symmetric scanning codes exist for this $8 \times 8$ grid?

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