
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 \(3 \times 3\) square grid is divided into nine \(1 \times 1\) squares. Each of the small squares is to be painted either green or red. In how many different ways can the painting be accomplished so that no green square shares its top or right side with any red square? There might be as few as zero or as many as nine small green squares.
A) 9  
B) 10  
C) 11  
D) 12  
E) 13

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