
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 $7 \times 7$ chessboard has 2 squares painted yellow, and the remaining squares painted green. If one coloring can be obtained from another through rotation in the plane of the chessboard, then the two colorings are considered the same. How many different colorings are possible?

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