
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 unit square of a 4-by-4 unit-square grid is to be colored either blue or red, with each color being equally likely. Calculate the probability that the resulting grid does not contain any 2-by-2 square of red squares, and express this probability in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.

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