
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 new scanning code is designed on a $9 \times 9$ grid of squares, some of which are colored black and others white. There must be at least one square of each color. A scanning code is symmetric if its appearance remains the same under rotation by multiples of $90^\circ$ counterclockwise about its center and under reflections across lines joining opposite corners or midpoints of opposite sides. Determine the total number of possible symmetric scanning codes for this $9\times9$ grid.

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