
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 a $9 \times 9$ grid of squares, with some squares colored black and the rest colored white. There must be at least one square of each color in this grid of $81$ squares. A scanning code is called $\textit{symmetric}$ if its appearance does not change when the entire square is rotated by $180^\circ$ around its center. What is the total number of possible symmetric scanning codes?

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