
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. Each of the small squares is to be painted either green or red. Determine the number of different ways the painting can be accomplished so that no green square shares its top, right, or bottom side with any red square.

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