
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 pattern consists of an $8 \times 8$ grid of squares, where each square can be colored red, blue, or white. A pattern is termed symmetric if it looks the same when the grid is rotated by $180^{\circ}$ around its center or reflected across the central horizontal or vertical line. Determine the total number of symmetric patterns possible if at least one square of each color is used.

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