
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 grid needs to be painted either green or red in each of its nine 1 by 1 squares, subject to the condition that no green square can share its bottom or left side with any red square. Determine the total number of ways the squares can be colored under these conditions.

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