
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 Cat Tom a birthday pie in the shape 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 both fish and sausage in one piece, which he did not mark (all other pieces are without filling). 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 at most one piece with sausage.

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

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