
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
A mouse named Jerry decided to gift a cat named Tom a birthday cake 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 was not marked. 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 cake pieces Tom needs to eat to guarantee that he gets the piece with both fish and sausage?

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