
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
Given a 3x3 grid, shading exactly three squares, and considering patterns that can be matched by rotations as not different but those matched by flips as different, calculate the number of distinct patterns.

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