
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
Consider an $8 \times 8$ grid of squares, with some colored black and others white. Each square must have at least one square of each color. A scanning code is symmetric if it looks the same when rotated by $90^\circ$, $180^\circ$, or $270^\circ$, and when reflected across any line joining midpoints of opposite sides. Additionally, it must remain unchanged when reflected across both diagonals. Determine the total number of possible symmetric scanning codes.

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