
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
Hernan wants to paint a  $8\times 8$  board such that every square is painted with blue or red. Also wants to every  $3\times 3$  subsquare have exactly  $a$  blue squares and every  $2\times 4$  or  $4\times 2$  rectangle have exactly  $b$  blue squares. Find all couples  $(a,b)$  such that Hernan can do the required.

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