
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 digital pattern consists of an $8 \times 8$ grid of squares, with some squares colored black and the rest colored white. There must be at least one square of each color. A pattern is considered symmetric if it looks the same when the entire square is rotated by a multiple of $90^\circ$ counterclockwise around its center, or when it is reflected across a line joining opposite corners or a line joining midpoints of opposite sides. Determine the total number of possible symmetric digital patterns.

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