
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
Each cell in a 4-by-4 grid is to be colored either green or yellow. For each cell, either color is equally likely to be used. The probability of obtaining a grid that does not have a 3-by-3 green square is $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p + q$.

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