
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 3 by 3 square is divided into nine 1 by 1 squares. In how many different ways can the painting be accomplished so that no green square shares any side (top, bottom, left, or right) with any red square?

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