
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
In a $7 \times 7$ grid, some squares are painted black and the rest are painted white, with at least one square of each color. A pattern is called "symmetric" if it looks the same when rotated $90^{\circ}$ and if it can be folded along either diagonal such that the two halves match. Find the total number of symmetric patterns.

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