
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
Mouse Jerry decided to give Tom the cat a birthday cake in the form of an $8 \times 8$ square. He placed fish in three pieces marked with the letter "P," sausage in two pieces marked with the letter "K," and added both in one piece but did not mark it (all other pieces are plain). Jerry also informed Tom that in any $6 \times 6$ square there are at least 2 pieces with fish, and in any $3 \times 3$ square there is no more than one piece with sausage.

What is the minimum number of pieces Tom needs to eat to ensure that he gets a piece with both fish and sausage?

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