
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
On a \(3 \times 3\) grid of 9 squares, each square is to be painted with either Red or Blue. If \(\alpha\) is the total number of possible colorings in which no \(2 \times 2\) grid consists of only Red squares, determine the value of \(\alpha\).

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