
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

Every day, Fröken Bock bakes a square cake of size \(3 \times 3\). Karlsson immediately cuts out four square pieces of size \(1 \times 1\) with sides parallel to the sides of the cake (not necessarily along the lines of the \(3 \times 3\) grid). After this, Little Boy cuts out a square piece from the remaining part of the cake, also with sides parallel to the sides of the cake. What is the largest piece of cake that Little Boy can get regardless of Karlsson’s actions?

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