
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

Petya cut out three $2 \times 2$ squares from a grid square $8 \times 8$, as shown in the picture. Olya wants to cut out (along the grid lines) as many $1 \times 3$ rectangles as possible from the remaining part of the square. What is the maximum number of such rectangles she can cut out?

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