
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
Every cell of a  $3\times 3$  board is coloured either by red or blue. Find the number of all colorings in which there are no  $2\times 2$  squares in which all cells are red.

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