
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 \(3 \times 3\). Karlson 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 that, Kid cuts out a square piece for himself 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 Kid can expect, regardless of Karlson's actions?

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